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MENSURATION, , QUESTIONS ASKED IN PREVIOUS SSC EXAMS, TYPE -I, 1. If the length of the diagonal AC of, a square ABCD is 5.2 cm, then, the area of the square is :, (1) 15.12 sq.cm, (2) 13.52 sq.cm, (3) 12.62 sq.cm, (4) 10.00 sq.cm., (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 2. The length of the diagonal of a, square is ‘a’ cm. Which of the following represents the area of the, square (in sq. cm.) ?, , a, , (1) 2a, , (2), , (3) a2/2, , (4) a2/4, , 2, , (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting), , 3. The diagonal of a square is 4 2, cm. The diagonal of another, square whose area is double, that of the first square is :, (1) 8 2 cm, , (2) 16 cm, , (3), , (4) 8 cm, , 32 cm, , 7. The perimeter of five squares are, 24 cm, 32 cm, 40 cm, 76 cm, and 80 cm respectively. The perimeter of another square equal, in area to sum of the areas of, these squares is :, (1) 31 cm, (2) 62 cm, (3) 124 cm, (4) 961 cm, (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 8. The ratio of the area of a square, to that of the square drawn on, its diagonal is :, (1) 1 : 1, (2) 1 : 2, (3) 1 : 3, (4) 1 : 4, (SSC CGL Prelim Exam. 13.11.2005, (First Sitting), , 9. From four corners of a square, sheet of side 4 cm, four pieces,, each in the shape of arc of a circle with radius 2 cm, are cut out., The area of the remaining portion is :, (1) (8–p) sq.cm., (2) (16–4p) sq.cm., (3) (16–8p) sq.cm., (4) (4–2 p)sq.cm., FCI Assistant Grade-III, Exam. 05.02.2012 (Paper-I), , (SSC CGL Prelim Exam. 24.02.2002 &, 13.11.2005 (IInd Sitting), , 4. The diagonal of a square A is, (a+b). The diagonal of a square, whose area is twice the area of, square A, is, (1) 2 (a+b), (2) 2 (a+b)2, (3), , 2 (a+b), , (4), , 2 (a-b), , (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone), , 5. The difference of the areas of two, squares drawn on two line, segments of different lengths is, 32 sq.cm. Find the length of the, greater line segment if one is, longer than the other by 2 cm., (1) 7 cm, (2) 9 cm, (3) 11 cm (4) 16 cm, (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 6. If the diagonals of two squares are, in the ratio of 2 : 5, their area will, be in the ratio of, (1), , 2: 5, , (3) 4 : 25, , (2) 2 : 5, (4) 4 : 5, , (SSC Section Officer (Commercial, Audit) Exam. 16.11.2003), , East Zone (IInd Sitting), , 10. The length of diagonal of a square, is 15 2 cm. Its area is, (1) 112.5 cm2, (3), , (2) 450 cm2, , 225 2, cm2 (4) 225 cm2, 2, , 11. A kite in the shape of a square, with a diagonal 32 cm attached, to an equilateral triangle of the, base 8 cm. Approximately how, much paper has been used to, make it? (Use 3 = 1.732), (1), (2), (3), (4), , 539.712, 538.721, 540.712, 539.217, , cm2, cm2, cm2, cm2, , (SSC CHSL DEO & LDC, Exam. 27.10.2013 IInd Sitting), (SSC CHSL DEO & LDC, Exam. 28.11.2010 (IInd Sitting), , 12. The breadth of a rectangular hall, is three-fourth of its length. If the, area of the floor is 768 sq. m.,, then the difference between the, length and breadth of the hall is:, , SME–1114, , (1) 8 metres (2) 12 metres, (3) 24 metres (4) 32 metres, (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 13. The length of a plot is five times, its breadth. A playground measuring 245 square metres occupies half of the total area of the, plot. What is the length of the, plot?, (1) 35 2 metres (2)175 2 metres, (3) 490 metres (4) 5 2 metres, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , 14. The length of a rectangular garden, is 12 metres and its breadth is 5, metres. Find the length of the, diagonal of a square garden, having the same area as that of, the rectangular garden :, (1) 2 30 m, , (2), , (3) 13 m, , (4) 8 15 m, , 13 m, , (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 15. A circular wire of diameter 42 cm, is folded in the shape of a rectangle whose sides are in the ratio 6 : 5 . Find the area enclosed, by the rectangle. (Take p =, (1) 540 cm2, (3) 2160 cm2, , 22, ), 7, , (2) 1080 cm2, (4) 4320 cm2, , (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone) & (SSC CGL Prelim, Exam. 13.11.2005 (IInd Sitting), , 16. A took 15 sec. to cross a, rectangular field diagonally, walking at the rate of 52 m/min., and B took the same time to, cross the same field along its, sides walking at the rate of 68 m/, min. The area of the field is :, (1) 30 m2 (2) 40 m2, (3) 50 m2 (4) 60 m2, (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 17. The difference between the length, and breadth of a rectangle is 23, m. If its perimeter is 206 m, then, its area is, (1) 1520 m2, (2) 2420 m2, 2, (3) 2480 m, (4) 2520 m2, (SSC Section Officer (Commercial, Audit) Exam. 16.11.2003)

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MENSURATION, 18. There is a rectangular tank of, length 180 m and breadth 120, m in a circular field. If the area, of the land portion of the field is, 40000 m2, what is the radius of, , 22, ), 7, (2) 135 m, (4) 145 m, , the field ? (Take p =, (1) 130 m, (3) 140 m, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 19. The length of a rectangular hall, is 5m more than its breadth. The, area of the hall is 750m2. The, length of the hall is :, (1) 15 m, (2) 22.5 m, (3) 25 m, (4) 30 m, (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 20. If the length and breadth of a, rectangle are in the ratio, 3 : 2 and its perimeter is 20 cm,, then the area of the rectangle (in, cm2) is :, (1) 24, (2) 48, (3) 72, (4) 96, , 24. A street of width 10 metres surrounds from outside a rectangular garden whose measurement, is 200 m × 180 m. The area of, the path (in square metres) is, (1) 8000, (2) 7000, (3) 7500, (4) 8200, (SSC Constable (GD) & Rifleman, (GD) Exam. 22.04.2012 (Ist Sitting), , 25. In measuring the sides of a rectangle, there is an excess of 5%, on one side and 2% deficit on, the other. Then the error percent in the area is, (1) 3·3%, (2) 3·0%, (3) 2·9%, (4) 2·7%, (SSC Multi-Tasking (Non-Technical), Staff Exam. 22.02.2011), , 26. A lawn is in the form of a rectangle having its breadth and length, in the ratio 3 : 4. The area of the, , 1, hectare. The breadth, 12, of the lawn is, (1) 25 metres (2) 50 metres, (3) 75 metres (4) 100 metres, lawn is, , (SSC CGL Prelim Exam. 13.11.2005, (First Sitting), , (SSC Graduate Level Tier-II, , 21. A path of uniform width runs, round the inside of a rectangular, field 38 m long and 32 m wide., If the path occupies 600m2, then, the width of the path is, (1) 30 m, (2) 5 m, (3) 18.75 m, (4) 10 m, , 27. The area of a rectangle is thrice, that of a square. The length of the, rectangle is 2 0 cm and the, , (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 22. The length and breadth of a rectangle are increased by 20% and, 25% respectively. The increase, in the area of the resulting rectangle will be :, (1) 60%, , (2) 50%, , (3) 40%, , (4) 30%, (SSC CHSL DEO & LDC, Exam. 27.11.2010), , 23. The length of a room floor exceeds, its breadth by 20 m. The area of, the floor remains unaltered when, the length is decreased by 10 m, but the breadth is increased by, 5 m. The area of the floor (in, square metres) is :, (1) 280, (2) 325, (3) 300, , (4) 420, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (East Zone), , Exam. 29.09.2013, , 3, 2, times that of the side of the, square. The side of the square,, (in cm) is, (1) 10, (2) 20, (3) 30, (4) 60, , breadth of the rectangle is, , 30. If the area of a triangle is 1176, cm 2 and base : corresponding, altitude is 3 : 4, then the altitude, of the triangle is :, (1) 42 cm, (2) 52 cm, (3) 54 cm, (4) 56 cm, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 31. The base of a triangle is 15 cm, and height is 12 cm. The height, of another triangle of double the, area having the base 20 cm is :, (1) 9 cm, (2) 18 cm, (3) 8 cm, (4) 12.5 cm, (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 32. The sides of a triangle are 3 cm,, 4 cm and 5 cm. The area (in, cm2) of the triangle formed by, joining the mid points of this triangle is :, (1) 6, (2) 3, (3), , 3, 2, , (4), , 3, 4, , (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 33. If D and E are the mid-points of, the side AB and AC respectively, of the DABC in the figure given, here, the shaded region of the, triangle is what per cent of the, whole triangular region?, , (SSC Graduate Level Tier-II, Exam. 29.09.2013, , 28. The length and breadth of a rectangular field are in the ratio 7 :, 4. A path 4 m wide running all, around outside has an area of 416, m2 . The breadth (in m) of the, field is, (1) 28, (2) 14, (3) 15, (4) 16, (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 29. ABC is a triangle with base AB., D is a point on AB such that AB, = 5 and DB = 3. What is the ratio of the area of D ADC to the, area of DABC ?, (1) 3/2, (2) 2/3, (3) 3/5, (4) 2/5, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , SME–1115, , (1) 50%, (3) 75%, , (2) 25%, (4) 60%, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 34. The ratio of base of two triangles, is x : y and that of their areas, is a : b. Then the ratio of their, corresponding altitudes will be:, (1), , a b, :, x y, , (3) ay : bx, , (2) ax : by, (4), , x b, :, a y, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting)

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MENSURATION, 35. The diagonal of a right angle isosceles triangle is 5 cm. Its area will, be, (1) 5 sq.cm, (2) 6.25 sq.cm, (3) 6.50 sq.cm (4) 12.5 sq.cm, (SSC Section Officer (Commercial Audit), Exam. 25.09.2005), , 36. In an isosceles triangle, the measure of each of equal sides is 10, cm and the angle between them, is 45°. the area of the triangle is, (1) 25 cm2, , 25, (2), 2 cm2, 2, , (3) 25 2 cm2 (4) 25 3 cm2, (SSC CPO S.I. Exam. 03.09.2006), , 37. From a point in the interior of an, equilateral triangle, the length of, the perpendiculars to the three, sides are 6 cm, 8 cm and 10 cm, respectively. The area of the triangle is, (1) 48 cm2, , (2) 16 3 cm2, , (3) 192 3 cm2 (4) 192 cm2, (SSC Section Officer (Commercial, Audit) Exam. 30.09.2007, (Second Sitting), , 38. The area of two equilateral triangles are in the ratio 25 : 36. Their, altitudes will be in the ratio :, (1) 36 : 25, (2)25 : 36, (3) 5 : 6, , (4) 5 : 6, , (SSC CPO S.I. Exam. 16.12.2007), , 39. ABC is an equilateral triangle of, side 2 cm. With A, B, C as centre, and radius 1 cm three arcs are, drawn. The area of the region, within the triangle bounded by, the three arcs is, , pI, FG, J cm, H, 2K, F 3p IJ cm, (2) GH 3 2K, F pI, (3) GH 3 - JK cm, 2, Fp I, (4) GH - 3 JK cm, 2, (1) 3 3 -, , 2, , 2, , 2, , 2, , 41. The sides of a triangle are in the, ratio 2 : 3 : 4. The perimeter of, the triangle is 18 cm. The area (in, cm2) of the triangle is, (1) 9, (2) 36, (3), , (4) 3 15, , 42, , (SSC CGL Tier-1 Exam. 19.06.2011, (Second Sitting), , 42. If the numerical value of the perimeter of an equilateral triangle, is, , 3 times the area of it, then, the length of each side of the triangle is, (1) 2 units, (2) 3 units, (3) 4 units, (4) 6 units, FCI Assistant Grade-III, Exam. 25.02.2012 (Paper-I), North Zone (Ist Sitting), , 43. Each side of an equilateral triangle is 6 cm. Find its area., (1) 9 3 sq.cm. (2) 6 3 sq.cm., (3) 4 3 sq.cm. (4) 8 3 sq.cm., FCI Assistant Grade-III, Exam. 05.02.2012 (Paper-I), East Zone (IInd Sitting), , 44. If a triangle with base 8 cm has, the same area as a circle with, radius 8 cm, then the corresponding altitude (in cm) of the, triangle is, (1) 12p, (2) 20p, (3) 16p, (4) 32p, (SSC Data Entry Operator, Exam. 02.08.2009), , 45. The measures (in cm) of sides of, a right angled triangle are given, by consecutive integers. Its area, (in cm2) is, (1) 9, (2) 8, (3) 5, (4) 6, (SSC Data Entry Operator, Exam. 02.08.2009), , 46. The area of an equilateral triangle is 4 3 cm 2 . The length of, each side of the triangle is :, (1) 3 cm, , (2) 2 2 cm, , (3) 2 3 cm, , (4) 4 cm, , (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , (SSC CHSL DEO & LDC, Exam. 27.11.2010), , 40. The area of a right-angled isosceles triangle having hypotenuse, , 47. The length of three medians of a, triangle are 9 cm, 12 cm and 15, cm. The area (in sq. cm) of the, triangle is, (1) 24, (2) 72, (3) 48, (4) 144, , 16 2 cm is, (1) 144 cm2, (3) 112 cm2, , (2) 128 cm2, (4) 110 cm2, , (SSC (South Zone) Investigator, Exam. 12.09.2010), , (SSC Graduate Level Tier-II, Exam.16.09.2012), , SME–1116, , 48. The area of the triangle formed, by the straight line 3x + 2y = 6, and the co-ordinate axes is, (1) 3 square units, (2) 6 square units, (3) 4 square units, (4) 8 square units, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 49. The ratio of length of each equal, side and the third side of an isosceles triangle is 3 : 4. If the area, of the triangle is 18 5 square, units, the third side is, (1) 16 units, (3) 8, , (2) 5, , 10 units, , 2 units (4) 12 units, (SSC CHSL DEO & LDC Exam., 21.10.2012 (Ist Sitting), , 50. The ratio of sides of a triangle is, 3 : 4 : 5. If area of the triangle is, 72 square unit, then the length, of the smallest side is :, (1) 4 3 unit, , (2) 5 3 unit, , (3) 6 3 unit, , (4) 3 3 unit, , (SSC CHSL DEO & LDC Exam., 21.10.2012 (IInd Sitting), , 51. If the length of each side of an, equilateral triangle is increased by, 2 unit, the area is found to be, increased by 3 + 3 square unit., The length of each side of the triangle is, (1), , 3 unit, , (2) 3 unit, , (3) 3 3 unit (4) 1 + 3 3 unit, (SSC CHSL DEO & LDC Exam., 28.10.2012 (Ist Sitting), , 52. What is the area of the triangle, whose sides are 9cm, 10cm and, 11cm?, (1) 30 cm2, (2) 60cm2, (3) 30 2 cm2, , (4) 60 2 cm2, , (SSC CHSL DEO & LDC Exam., 28.10.2012 (Ist Sitting), , 53. The area of an isosceles triangle, is 4 square unit. If the length of, the third side is 2 unit, the length, of each equal side is, (1) 4 units, (3), , (2) 2 3 units, , 17 units (4) 3 2 units, (SSC CHSL DEO & LDC Exam., 28.10.2012 (Ist Sitting)

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MENSURATION, 54. The ratio of sides of a triangle is, 3:4:5 and area of the triangle is, 72 square unit. Then the area of, an equilateral triangle whose perimeter is same as that of the previous triangle is, (1) 32 3 square units, (2) 48 3 square units, (3) 96 square units, (4) 60 3 square units, (SSC CHSL DEO & LDC Exam., 04.11.2012 (IInd Sitting), , 55. A right angled isosceles triangle, is inscribed in a semi-circle of, radius 7 cm. The area enclosed, by the semi-circle but exterior to, the triangle is, (1) 14 cm2, (2) 28 cm2, (3) 44 cm2, (4) 68 cm2, (SSC Delhi Police S.I., Exam. 19.08.2012), , 56. What is the area of a triangle, having perimeter 32cm, one side, 11cm and difference of other two, sides 5cm?, (1) 8 30 cm, , 2, , (2) 5 35 cm, , (3) 6 30 cm, , 2, , (4) 8 2 cm2, , 2, , 60. The sides of a triangle are 16 cm,, 12 cm and 20 cm. Find the area., (1) 64 cm2, (2) 112 cm2, 2, (3) 96 cm, (4) 81 cm2, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 61. 360 sq. cm and 250 sq. cm are, the area of two similar triangles., If the length of one of the sides, of the first triangle be 8 cm, then, the length of the corresponding, side of the second triangle is, (1) 6, , 1, cm, 5, , 2, (3) 6, cm, 3, , (2) 6, , 1, cm, 3, , (4) 6 cm, , (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 62. The perimeter of an isosceles triangle is 544 cm and each of the, equal sides is, , 5, times the base., 6, , What, is, the, (in cm2) of the triangle ?, (1) 38172, (2) 18372, (3) 31872, (4) 13872, , area, , (SSC Delhi Police S.I. (SI), Exam. 19.08.2012), , (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 57. The area (in sq. unit) of the triangle formed in the first quadrant by the line 3x + 4y = 12 is, (1) 8, (2) 12, (3) 6, (4) 4, , 63. The altitude drawn to the base of, an isosceles triangle is 8 cm and, its perimeter is 64 cm. The area, (in cm2) of the triangle is, (1) 240, (2) 180, (3) 360, (4) 120, , (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , 58. The height of an equilateral triangle is 15 cm. The area of the, triangle is, (1) 50 3 sq. cm., (2) 70 3 sq. cm., (3) 75 3 sq. cm., (4) 150 3 sq. cm., (SSC Graduate Level Tier-I, Exam. 19.05.2013), , 59. The area of an equilateral triangle, is 9 3 m2. The length (in m) of, the median is, (1) 2 3, , (2) 3 3, , (3) 3 2, , (4) 2 2, (SSC Graduate Level Tier-II, Exam. 29.09.2013, , (SSC CHSL DEO & LDC Exam., 10.11.2013, IInd Sitting), , 64. The perimeter of a rhombus is, 40 m and its height is 5 m. Its, area is :, (1) 60 m2 (2) 50 m2, (3) 45 m2 (4) 55m2, (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 66. The area of a rhombus is 150, cm2. The length of one of its diagonals is 10 cm. The length of, the other diagonal is :, (1) 25 cm, (2) 30 cm, (3) 35 cm, (4) 40 cm, (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 67. The perimeter of a rhombus is, 100 cm. If one of its diagonals is, 14 cm, then the area of the, rhombus is, (1) 144 cm2, (2) 225 cm2, 2, (3) 336 cm, (4) 400 cm2, (SSC Data Entry Operator, Exam. 31.08.2008), , 68. If the measure of one side and, one diagonal of a rhombus are 10, cm and 16 cm respectively, then, its area (in cm2) is :, (1) 60, (2) 64, (3) 96, (4) 100, (SSC CHSL DEO & LDC Exam., 28.11.2010 (Ist Sitting), , 69. The ratio of the length of the, parallel sides of a trapezium is, 3:2. The shortest distance, between them is 15 cm. If the, area of the trapezium is 450 cm2,, the sum of the length of the, parallel sides is, (1) 15 cm, (2) 36 cm, (3) 42 cm, , (4) 60 cm, , (SSC Multi-Tasking (Non-Technical), Staff Exam. 27.02.2011), , 70. A parallelogram has sides 15 cm, and 7 cm long. The length of one, of the diagonals is 20 cm. The, area of the parallelogram is, (1) 42 cm2, (2) 60 cm2, (3) 84 cm2, , (4) 96 cm2, , (SSC Multi-Tasking (Non-Technical), Staff Exam. 27.02.2011), , 71. Sides of a parallelogram are in the, ratio 5 : 4. Its area is 1000 sq., units. Altitude on the greater side, is 20 units. A ltitude on the, smaller side is, (1) 30 units, (2) 25 units, (3) 10 units, , (4) 15 units, , 65. The area of a field in the shape, of a trapezium measures 1440, m2. The perpendicular distance, between its parallel sides is 24, m. If the ratio of the parallel, sides is 5 : 3, the length of the, longer parallel side is :, (1) 75 m, (2) 45 m, (3) 120 m, (4) 60 m, , 72. The perimeter of a rhombus is, 40 cm and the measure of an, angle is 60°, then the area of, it is :, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (Delhi Zone), , SME–1117, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (Delhi Zone), , (1) 100, , 2, 3 cm (2) 50, , (3) 160, , 2, 2, 3 cm (4) 100 cm, , 2, 3 cm

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MENSURATION, 73. The parallel sides of a trapezium, are in a ratio 2 : 3 and their, shortest distance is 12 cm. If the, area of the trapezium is 480 sq., cm., the longer of the parallel, sides is of length :, (1) 56 cm, (2) 36 cm, (3) 42 cm, (4) 48 cm, (SSC CHSL DEO & LDC Exam., 21.10.2012 (IInd Sitting), , 74. If the sum of the length, breadth, and height of a rectangular, parallelopiped is 24 cm and the, length of its diagonal is 15 cm,, then its total surface area is, (1) 256 cm2, (2) 265 cm2, (3) 315 cm2, (4) 351 cm2, (SSC Multi-Tasking Staff, Exam. 17.03.2013, IInd Sitting), , 75. The perimeter of a non-square, rhombus is 20 cm. One of its diagonal is 8 cm. The area of the, rhombus is, (1) 28 sq cm, (2) 20 sq cm, (3) 22 sq cm, (4) 24 sq cm, (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , 76. The perimeter of a rhombus is, 100 cm and one of its diagonals, is 40 cm. Its area (in cm2) is, (1) 1200, (2) 1000, (3) 600, (4) 500, (SSC CHSL DEO & LDC Exam., 27.10.2013 IInd Sitting), , 77. In • ABC, D and E are the points, of sides AB and BC respectively, such that DE || AC and AD : DB, = 3 : 2. The ratio of area of trapezium ACED to that of D BED is, (1) 4 : 15, (2) 15 : 4, (3) 4 : 21, (4) 21 : 4, (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 78. ABCD is a trapezium in which, AB||DC and AB = 2 CD. The, diagonals AC and BD meet at O., The ratio of area of triangles AOB, and COD is, (1) 1 : 1, , (2) 1 : 2, , (3) 4 : 1, , (4) 1 : 4, , (SSC CHSL DEO & LDC Exam., 10.11.2013, IInd Sitting), , 79. The length of each side of a, rhombus is equal to the length of, the side of a square whose, diagonal is 40 2 cm. If the, length of the diagonals of the, rhombus are in the ratio 3 : 4,, then its area (in cm2) is, (1) 1550, (2) 1600, (3) 1535, (4) 1536, (SSC CHSL DEO & LDC Exam., 10.11.2013 (IInd Sitting), , 80. The area of a regular hexagon of, side 2 3 cm is :, (1) 18 3 cm2 (2) 12 3 cm2, (3) 36 3 cm2 (4) 27 3 cm2, (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 81. Each side of a regular hexagon, is 1 cm. The area of the hexagon, is, (1), , 3 3, cm2, 2, , (3) 4 3 cm2, , (2), , 3 3, cm2, 4, , (4) 3 2 cm2, , (SSC CPO S.I. Exam. 05.09.2004), , 82. An equilateral triangle of side 6, cm has its corners cut off to form, a regular hexagon. Area (in cm2), of this regular hexagon will be, (1) 3 3, , (2) 3 6, , (3) 6 3, , (4), , 5 3, 2, , (SSC CGL Tier-I Exam. 16.05.2010, (First Sitting), , 83. The ratio of the area of a regular, hexagon and an equilateral triangle having same perimeter is, (1) 2: 3, (2) 6: 1, (3) 3: 2, (4) 1: 6, (SSC MTS (Non-Technical, Exam. 20.02.2011) & (SSC, CHSL DEO & LDC Exam. 04.12.2011, (Ist Sitting (East Zone), , 84. The area of a sector of a circle, of radius 5 cm, formed by an, arc of length 3.5 cm is :, (1) 8.5 cm2, (2) 8.75 cm2, (3) 7.75 cm2 (4) 7.50 cm2, (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting), , 85. The area (in sq. cm.) of the largest, circle that can be drawn inside, a square of side 28 cm, is :, (1) 17248, (2) 784, (3) 8624, (4) 616, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , 86. If the circumference of a circle, increases from 4 p to 8p, what, change occurs in its area?, (1) It doubles, (2) It triples, (3) It quadruples (4) It is halved, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , SME–1118, , 87. The area of the ring between two, concentric circles, whose, circumference are 88 cm and, 132 cm, is :, (1) 780 cm2, (2) 770 cm2, 2, (3) 715 cm, (4) 660 cm2, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 88. Three circles of radius 3.5 cm each, are placed in such a way that each, touches the other two. The area, of the portion enclosed by the, circles is, (1) 1.975 cm2 (2) 1.967 cm2, (3) 19.67 cm2 (4) 21.21 cm2, (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 89. The area of a circular garden is, 2464 sq.m. How much distance, will have to be covered if you like, to cross the garden along its di-, , 22, ), 7, (2) 48 m, (4) 24 m, , ameter ? (Use p =, (1) 56 m, (3) 28 m, , (SSC CPO S.I. Exam. 07.09.2003), , 90. Four equal circles each of radius, ‘a’ units touch one another. The, area enclosed between them, (p =, , 22, ), in square units, is, 7, , (1) 3a2, , (3), , 41a 2, 7, , (2), , 6a 2, 7, , (4), , a2, 7, , (SSC CPO S.I. Exam. 07.09.2003), , 91. Three coins of the same size (radius 1 cm) are placed on a table, such that each of them touches, the other two. The area enclosed, by the coins is, , FG p – 3 IJ cm2, H2 K, F pI 2, (2) GH 3 – JK cm, 2, pI, F, 2, (3) GH 2 3 – JK cm, 2, pI, F, 2, (4) GH 3 3 – JK cm, 2, (1), , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting)

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MENSURATION, 92. The area of the largest triangle,, that can be inscribed in a semicircle of radius r cm, is, (1) 2r cm2, (2) r2 cm2, (3) 2r2 cm2, , (4), , 1 2, r cm2, 2, , (SSC CPO S.I. Exam. 05.09.2004), , 93. The area of circle whose radius, is 6 cm is trisected by two concentric circles. The radius of the, smallest circle is, (1) 2 3 cm (2) 2 6 cm, (3) 2 cm, (4) 3 cm, , (1) 1, , 29, 29, cm2 (2) 2, cm 2, 48, 48, , (3) 1, , 27, 27, cm 2 (4) 2, cm 2, 48, 48, (SSC Data Entry Operator, Exam. 31.08.2008), , 98. A 7 m wide road runs outside, around a circular park, whose, circumference is 176 m. The area, of the road is :, , [use p =, , (1) 1386 m2, , (2) 1472 m2, , 94. The area of the shaded region in, the figure given below is, , (3) 1512 m2, , (4) 1760 m2, , FG, H, , IJ, K, , a2 p, - 1 sq. units, (1), 2 2, (2), , a2, , (3), , a2, , (4), , a2, (p – 1) sq. units, 2, , (p – 1) sq. units, , FG p - 1IJ sq. units, H2 K, , (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 95. The area of a circle is increased, by 22 cm its radius is increased, by 1 cm. The original radius of, the circle is, (1) 6 cm, (2) 3.2 cm, (3) 3 cm, (4) 3.5 cm, (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 96. The radius of circle A is twice that, of circle B and the radius of circle, B is twice that of circle C. Their, area will be in the ratio, (1) 16 : 4 : 1 (2) 4 : 2 : 1, (3) 1 : 2 : 4 (4) 1 : 4 : 16, (SSC CPO S.I. Exam. 06.09.2009), , 97. The circumference of a circle is, 11 cm and the angle of a sector, of the circle is 60°. The area of, , 22, the sector is (use p =, ), 7, , (SSC CHSL DEO & LDC Exam., 04.11.2012, IInd Sitting), , 104. The ratio between the area of two, circles is 4 : 7. What will be the, ratio of their radii?, (1) 2 :, , 22, ], 7, , (SSC CPO S.I. Exam. 03.09.2006), , C, , 103. The perimeter of a semicircular, path is 36 m. Find the area of, this semicircular path., (1) 42sq.m, (2) 54 sq. m, (3) 63 sq.m, (4) 77 sq. m, , (SSC CHSL DEO & LDC, Exam. 27.11.2010), , 99. The four equal circles of radius 4, cm drawn on the four corners of, a square touch each other externally. Then the area of the portion between the square and the, four sectors is, (1) 9 (p – 4) sq. cm., (2) 16 (p – 4) sq. cm., (3) 9 (4 – p) sq. cm., (4) 16 (4 – p) sq.cm., (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (North Zone), , 100. If the four equal circles of radius, 3 cm touch each other externally,, then the area of the regio n, bounded by the four circles is, (1) 4(9 – p) sq.cm, (2) 9(4 – p) sq.cm, (3) 5(6 – p) sq.cm, (4) 6(5 – p) sq.cm, (SSCCHSL DEO & LDC, Exam. 11.12.2011 (Ist Sitting, (East Zone), , 101. The area of a circle is increased, by 22 cm2 when its radius is increased by 1 cm. The original, radius of the circle is, (1) 3 cm, (2) 5 cm, (3) 7 cm, (4) 9 cm, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 102. The radii of two circles are 5cm, and 12cm. The area of a third, circle is equal to the sum of the, area of the two circles. The radius of the third circle is :, (1) 13 cm, (2) 21 cm, (3) 30 cm, (4) 17 cm, (SSC CHSL DEO & LDC Exam., 21.10.2012 (IInd Sitting), , SME–1119, , (2) 4 : 7, , 7, , (3) 16 : 49, , (4) 4 :, , 7, , (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , 105. Three circles of radius a, b, c, touch each other externally. The, area of the triangle formed by, joining their centre is, (1), , (a + b + c )abc, , (2) (a + b + c ) ab + bc + ca, (3) ab + bc + ca, (4) None of the above, (SSC Graduate Level Tier-I, Exam. 21.04.2013 IInd Sitting), , 106. The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm, is drawn within a larger circle, of radius 5 cm. Find the ratio of, the area of the annular zone to, the area of the larger circle. (Area, of the annular zone is the difference between the area of the, larger circle and that of the, smaller circle)., (1) 9 : 16, , (2) 9 : 25, , (3) 16 : 25, , (4) 16 : 27, , (SSC Graduate Level Tier-I, Exam. 21.04.2013 IInd Sitting), , 107. The diameter of two circles are, the side of a square and the diagonal of the square. The ratio of, the area of the smaller circle and, the larger circle is, (1) 1 : 2, (3), , 2 :, , (2) 1 : 4, , 3, , (4) 1 :, , 2, , (SSC Graduate Level Tier-I, Exam. 19.05.2013 Ist Sitting)

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MENSURATION, 108. Three circles of equal radius ‘a’, cm touch each other. The area of, the shaded region is :, , 112. The area of the incircle of an, equilateral triangle of side 42 cm, is, , FG Take p = 22 IJ, H, 7 K, , (1) 231 cm2, (3) 22 3, , cm2, , :, , (2) 462cm2, (4) 924 cm2, , (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 113. The ratio of the area of the in-circle and the circum-circle of a, square is, , F 3 + p I a sq.cm, (1) G, H 2 JK, F 6 3 – p I a sq.cm, (2) G, H 2 JK, (3) e 3 – p ja sq.cm, F 2 3 - p I a sq.cm, (4) G, H 2 JK, 2, , 2, , 2, , 2, , (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 109. The radii of two circles are 10, cm and 24 cm. The radius of a, circle whose area is the sum of, the area of these two circles is, (1) 36 cm, (2) 17 cm, (3) 34 cm, (4) 26 cm, (SSC CHSL DEO & LDC Exam., 10.11.2013, IInd Sitting), , 110. The area of the greatest circle inscribed inside a square of side 21, cm is (Take p =, , 22, ), 7, , (1) 344.5 cm2, (3) 346.5 cm2, , (2) 364.5 cm2, (4) 366.5 cm2, , (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 111. The area of the greatest circle,, which can be inscribed in a, square whose perimeter is 120, cm, is :, , b g, 2, 22 F 7 I, ´ G J cm, (2), 7 H 2K, 2, 22 F 15 I, ´ G J cm, (3), H 2K, 7, 2, 22 F 9 I, ´ G J cm, (4), 7 H 2K, , 22, 2, ´ 15 cm2, (1), 7, , (1) 1 : 2, (3) 1 :, , (2), , (SSC Section Officer (Commercial, , Audit) Exam. 26.11.2006, (IInd Sitting) & (SSC CHSL DEO &, LDC Exam. 11.12.2011, (IInd Sitting, Delhi Zone), , 114. The area of an equilateral triangle, inscribed in a circle is 4 3 cm2., The area of the circle is, , 2, , 2, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 119. The sides of a triangle are 6 cm,, 8 cm and 10 cm. The area of the, greatest square that can be inscribed in it, is, (1) 18 cm2, (2) 15 cm2, (3), , 2304, 576, cm2 (4), cm 2, 49, 50, , (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 120. The length of a side of an equilateral triangle is 8 cm. The area, of the region lying between the, circumference and the incircle of, , 22, ), 7, , the triangle is (Use p =, , (1), , 16, p cm2, 3, , (2), , 22, p cm2, 3, , (1) 50, , (2) 50, , (3), , 28, p cm2, 3, , (4), , 32, p cm2, 3, , 1, cm2, 7, , (3) 75, , 1, cm2, 7, , (4) 75, , (SSC Section Officer (Commercial, , 2, cm2, 7, 2, cm2, 7, , Audit) Exam. 26.11.2006, (IInd Sitting) & (SSC SAS, Exam. 26.06.2010 (Paper-I), , 121. The length of each side of an, , 115. The area of the largest circle,, that can be drawn inside a rectangle with sides 18 cm. by 14, cm, is, (1) 49 cm2, (2) 154 cm2, (3) 378 cm2 (4) 1078 cm2, , equilateral triangle is 14 3 cm., The area of the incircle (in, cm2), is, (1) 450, (2) 308, (3) 154, (4) 77, , (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 116. A circle is inscribed in an equilateral triangle of side 8 cm. The, area of the portion between the, triangle and the circle is, (1) 11 cm2, (2) 10.95 cm2, 2, (3) 10 cm, (4) 10.50 cm2, (SSC Section Officer (Commercial, Audit) Exam. 30.09.2007, (Second Sitting), , 117. If the difference between areas, of the circumcircle and the incircle of an equilateral triangle is 44, cm2, then the area of the trian-, , 2, , (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , 2 :1, , (4) 2: 1, , 2, , 118. If the area of a circle inscribed in, a square is 9p cm2,then the area, of the square is, (1) 24 cm2, (2) 30 cm2, (3) 36 cm2, (4) 81 cm2, , gle is, , FG Take p = 22 IJ, H, 7K, , (SSC CPO S.I. Exam. 09.11.2008), , (SSC CPO (SI, ASI & Intelligence Officer), Exam. 28.08.2011 Paper-I), , 122. The area of a circle inscribed in, a square of area 2 m2 is, (1), , p 2, m, 4, , (3) pm2, , (2), , p 2, m, 2, , (4) 2pm2, , FCI Assistant Grade-III, Exam. 25.02.2012 (Paper-I), North Zone (Ist Sitting), , 123. Length of the perpendiculars from, a point in the interior of an equilateral triangle on its sides are 3, cm, 4 cm and 5 cm. Area of the, triangle is, , (1) 28 cm2, , (2) 7 3 cm2, , (1) 48 3 cm2 (2) 54 3 cm2, , (3) 14 3 cm 2, , (4) 21 cm2, , (3) 72 3 cm2 (4) 80 3 cm2, , (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , SME–1120, , (SSC Data Entry Operator, Exam. 02.08.2009)

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MENSURATION, 124. The ratio of the areas of the circumcircle and the incircle of an, equilateral triangle is, (1) 2 : 1, (2) 4 : 1, (3) 8 : 1, (4) 3 : 2, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting, (North Zone), , 125. Area of the incircle of an equilateral triangle with side 6 cm is, , p, sq. cm. (2) 3 p sq. cm., 2, (3) 6p sq. cm. (4) 3p sq. cm., , 131. The areas of a square and a rectangle are equal. The length of, the rectangle is greater than the, length of any side of the square, by 5 cm and the breadth is less, by 3 cm. Find the perimeter of, the rectangle., (1) 17 cm, (2) 26 cm, (3) 30 cm, (4) 34 cm, (SSC CGL Prelim Exam. 24.02.2002, (IInd Sitting) & (SSC CGL Prelim, Exam. 13.11.2005 (Ist Sitting)), , (1), , (SSC CHSL DEO & LDC, Exam. 04.12.2011, (IInd Sitting (East Zone), , 126. The area of the square inscribed, in a circle of radius 8 cm is, (1) 256 sq. cm (2) 250 sq. cm, (3) 128 sq. cm (4) 125 sq. cm, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 127. A circle is inscribed in an equilateral triangle and a square is, inscribed in that circle. The ratio of the areas of the triangle, and the square is, (1), , 3 :4, , (3) 3 3 : 2, , (2), , 3 :8, , (4) 3 3 : 1, , (SSC Multi-Tasking Staff, Exam. 17.03.2013, IInd Sitting), , 128. The ratio of the area of an equilateral triangle and that of its, circumcircle is, (1) 2 3 : 2p, , (2) 4 : p, , (3) 3 3 : 4 p, , (4) 7 2 : 2p, , (SSC Multi-Tasking Staff, Exam. 24.03.2013, Ist Sitting), , 129. Between a square of perimeter, 44 cm and a circle of circumference 44 cm, which figure has, larger area and by how much?, (1) Square, 33cm2, (2) Circle, 33 cm2, (3) Both have equal area., (4) Square, 495 cm2, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , 130. The perimeter of a square and a, circular field are the same. If the, area of the circular field is 3850, sq metres,what is the area (in, m2) of the square?, (1) 4225, (2) 3025, (3) 2500, (4) 2025, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 132. If a wire is bent into the shape, of a square, the area of the, square is 81 sq. cm. When the, wire is bent into a semicircular, shape, the area of the semicircle, (taking p =, , 22, ) is :, 7, , (1) 154 cm2, (3) 44 cm2, , (2) 77 cm2, (4) 22 cm2, , (SSC CGL Prelim Exam. 24.02.2002, (IInd Sitting) & (SSC CGL Tier-I, Exam. 26.06.2011 (IInd Sitting), , 133. The perimeter of a rectangle is, 160 metre and the difference of, two sides is 48 metre. Find the, side of a square whose area is, equal to the area of this rectangle., (1) 32 m, (2) 8 m, (3) 4 m, (4) 16 m, (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone) & (SSC CGL Prelim, Exam. 13.11.2005 (Ist Sitting), , 134. If the area of a triangle with base, 12 cm is equal to the area of a, square with side 12 cm, the altitude of the triangle will be, (1) 12 cm, (2) 24 cm, (3) 18 cm, (4) 36 cm, (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone) & (SSC CGL Prelim, Exam. 13.11.2005 (Ist Sitting), , 135. The area (in m2) of the square, which has the same perimeter as, a rectangle whose length is 48, m and is 3 times its breadth, is :, (1) 1000, (2) 1024, (3) 1600, (4) 1042, (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 136. A square and an equilateral triangle are drawn on the same, base. The ratio of their area is, (1) 2 : 1, (2) 1 : 1, (3), , 3:4, , (4) 4 : 3, , (SSC CGL Prelim Exam. 13.11.2005, (Second Sitting), , SME–1121, , 137. A wire, when bent in the form of, a square, encloses a region having area 121 cm2. If the same, wire is bent into the form of a, circle, then the area of the circle, is, , FG Take p = 22 IJ, H, 7K, , (1) 144 cm2, (3) 154 cm2, , (2) 180 cm2, (4) 176 cm2, , (SSC CGL Prelim Exam. 27.07.2008, (Ist Sitting) & (SSC HSL DEO & LDC, Exam. 28.11.2010 (IInd Sitting), , 138. A copper wire is bent in the form, of an equilateral triangle and has, area 121 3 cm2. If the same wire, is bent into the form of a circle,, the area (in cm2) enclosed by the, wire is (Take p =, (1) 364.5, (3) 346.5, , 22, ), 7, , (2) 693.5, (4) 639.5, , (SSC CGL Tier-1 Exam. 19.06.2011, (First Sitting), , 139. A copper wire is bent in the shape, of a square of area 81cm2. If the, same wire is bent in the form of, a semicircle, the radius (in cm), 22, of the semicircle is (Take p = 7 ), (1) 16, (2) 14, , (3) 10, , (4) 7, , (SSC CGL Tier-1 Exam. 26.06.2011, (First Sitting), , 140. At each corner of a triangular, field of sides 26 m, 28 m and 30, m, a cow is tethered by a rope of, 2, length 7 m. The area (in m ), ungrazed by the cows is, (1) 336, (2) 259, (3) 154, (4) 77, , (SSC CGL Tier-1 Exam. 26.06.2011, (Second Sitting), , 141. An equilateral triangle is drawn, on the diagonal of a square. The, ratio of the area of the triangle to, that of the square is, (1), , 3 :2, , (3) 2 : 3, , (2), , 2: 3, , (4) 1 : 2, , (FCI Assistant Grade-III, Exam. 25.02.2012 (Paper-I), North Zone (Ist Sitting), , 142. A cow is tied on the corner of a, rectangular field of size 30 m ×20, m by a 14m long rope. The area, of the region, that she can graze,, , 22, ):, 7, (1) 350 m2, (2) 196 m2, (3) 154 m2, (4) 22 m2, is (use p =, , (SSC CHSL DEO & LDC, Exam. 28.11.2010 (Ist Sitting)

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MENSURATION, 143. A circle and a square have equal, areas. The ratio of a side of the, square and the radius of the circle is, (1) 1 : p, , (2), , (3) 1 : p, , (4) p : 1, , p :1, , (SSC CHSL DEO & LDC Exam., 28.11.2010 (IInd Sitting), , 144. If the perimeters of a rectangle, and a square are equal and the, ratio of two adjacent sides of the, rectangle is 1 : 2 then the ratio of, area of the rectangle and that of, the square is, (1) 1 : 1, (2) 1 : 2, (3) 2 : 3, (4) 8 : 9, (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 145. The perimeter of a triangle and, an equilateral triangle are same., Also, one of the sides of the, rectangle is equal to the side of, the triangle. The ratio of the area, of the rectangle and the triangle is, (1), , 3:1, , (3) 2 : 3, , (2) 1 : 3, (4) 4 : 3, , (SSC Constable (GD), Exam. 12.05.2013 Ist Sitting), , 146. The radius of a circle is a side of, a square. The ratio of the area of, the circle and the square is, (1) 1 : p, (2) p : 1, (3) p : 2, (4) 2 : p, (SSC Graduate Level Tier-I, Exam. 19.05.2013 Ist Sitting), , 147. If the length of a rectangle is, increased by 25% and the width, is decreased by 20%, then the, area of the rectangle :, (1) increases by 5%, (2) decreases by 5%, (3) remains unchanged, (4) increases by 10%, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 148. The length of a rectangle is decreased by 10% and its breadth, is increased by 10%. By what, per cent is its area changed ?, (1) 0%, (2) 1%, (3) 5%, (4) 100%, (SSC CGL Prelim Exam. 08.02.2004, (Ist Sitting) & (SSC CGL Tier-I, Exam. 16.05.2010 (Ist Sitting), , 149. The percentage increase in the, area of a rectangle, if each of its, sides is increased by 20%, is :, (1) 40%, (2) 42%, (3) 44%, (4) 46%, (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 150. If the circumference of a circle, is reduced by 50%, its area will, be reduced by, (1) 12.5%, (2) 25%, (3) 50%, (4) 75%, (SSC CPO S.I. Exam. 05.09.2004), , 151. If the side of a square is increased, by 25%, then its area is increased by :, (1) 25%, (2) 55%, (3) 40.5%, (4) 56.25%, (SSC CPO S.I. Exam. 26.05.2005), , 152. If the radius of a circle is increased by 50%, its area is increased by :, (1) 125%, (2) 100%, (3) 75%, (4) 50%, (SSC CGL Prelim Exam. 13.11.2005 (Ist, Sitting) & (SSC CGL Tier-I, Exam. 26.06.2010 (IInd Sitting), , 153. If the length of a rectangle is increased by 20% and its breadth, is decreased by 20%, then its, area, (1) increases by 4%, (2) decreases by 4%, (3) decreases by 1%, (4) remains unchanged, (SSC CPO S.I. Exam. 03.09.2006), , 154. If each side of a rectangle is increased by 50%, its area will be, increased by, (1) 50%, (2) 125%, (3) 100%, (4) 250%, (SSC CGL Prelim Exam. 04.02.2007, (IInd Sitting) & (SSC HSL DEO, & LDC Exam. 28.11.2010), , 155. If the altitude of a triangle is increased by 10% while its area remains same, its corresponding, base will have to be decreased, by, (1) 10 %, (2) 9 %, (3) 9, , 1, %, 11, , (4) 11, , 1, %, 9, , (SSC Section Officer (Commercial, Audit) Exam. 30.09.2007 (IInd, Sitting) & (SSC MTS Exam., 17.03.2013, Kolkata Region), , 156. If the circumference of a circle, is increased by 50% then the, area will be increased by, (1) 50%, (2) 75%, (3) 100%, (4) 125%, (SSC Section Officer (Commercial, Audit) Exam. 30.09.2007 (Second, Sitting ), , SME–1122, , 157. The length and breadth of a rectangle are increased by 12% and, 15% respectively. Its area will be, increased by :, (1) 27, , 1, %, 5, , (3) 27%, , (2) 28, , 4, %, 5, , (4) 28%, , (SSC CPO S.I. Exam. 16.12.2007), , 158. Each side of a rectangular field, is diminished by 40%. By how, much per cent is the area of the, field diminished ?, (1) 32%, (2) 64%, (3) 25%, (4) 16%, (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 159. The length of rectangle is increased by 60%. By what percent would the breadth to be decreased to maintain the same, area ?, , 1, %, 2, (3) 75%, , (1) 37, , (2) 60%, (4) 120%, , (SSC CPO S.I. Exam. 06.09.2009), , & (SSC MTS Exam. 17.03.2013,, Kolkata Region), , 160. If each side of a square is increased by 10%. its area will be, increased by, (1) 10%, (2) 21%, (3) 44%, (4) 100%, (SSC CGL Tier-I Exam. 16.05.2010, (IInd Sitting) & (SSC SAS Exam., 26.06.2010 (Paper-I), , 161. If the length of a rectangular plot, of land is increased by 5% and, the breadth is decreased by 10%,, how much will its area increase, or decrease ?, (1) 6.5% increase, (2) 5.5% decrease, (3) 5.5% increase, (4) 6.5% decrease, (SSC CPO S.I. Exam. 12.12.2010, (Paper-I), , 162. The radius of a circle is increased, by 1%. How much does the area, of the circle increase ?, (1) 1%, (2) 1.1%, (3) 2 %, (4) 2.01%, (SSC CHSL DEO & LDC Exam., 28.11.2010 (Ist Sitting), , 163. In measuring the sides of a rectangle, there is an excess of 5%, on one side and 2% deficit on, the other. Then the error percent in the area is, (1) 3·3%, (2) 3·0%, (3) 2·9%, (4) 2·7%, (SSC Multi-Tasking (Non-Technical), Staff Exam. 20.02.2011)

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MENSURATION, 164. The length and breadth of a, square are increased by 30% and, 20% respectively. The area of the, rectangle so formed exceeds the, area of the square by, (1) 46%, (2) 66%, (3) 42%, (4) 56%, (SSC CHSL DEO & LDC Exam., 04.11.2012, Ist Sitting), , 165. If each edge of a cube is increased, by 40%, the percentage increase, in its surface area is, (1) 40%, (2) 60%, (3) 80%, (4) 96%, (SSC Multi-Tasking Staff Exam., 10.03.2013, Ist Sitting : Patna), , 166. If the diameter of a circle is increased by 8%, then its area is, increased by :, (1) 16.64%, (2) 6.64%, (3) 16%, (4) 16.46%, (SSC Multi-Tasking Staff, Exam. 10.03.2013), , 167. One side of a square is increased, by 30%. To maintain the same, area, the other side will have to, be decreased by, (1) 23, , 1, %, 13, , (3) 30%, , (2) 76, , 12, %, 13, , (4) 15%, , (SSC Graduate Level Tier-I, Exam. 21.04.2013 IInd Sitting)), , 168. The length and breadth of a rectangle are doubled. Percentage increase in area is, (1) 150%, (2) 200%, (3) 300%, (4) 400%, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 169.ABC is an equilateral triangle. P, and Q are two points on AB and, AC respectively such that PQ ||, BC . If PQ = 5 cm, then area of, DAPQ is :, , (1), , (3), , 25, sq. cm, 4, , (2), , 25, 3, , sq. cm, , 25 3, sq. cm (4) 25 3 sq. cm, 4, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (East Zone), , 170. If area of an equilateral triangle, is a and height b, then value of, , b2, is:, a, , (1) 3, , (3), , (2), , 3, , (4), , (1) 15 cm, (3) 42 cm, , 1, 3, , (SSC Multi-Tasking (Non-Technical), Staff Exam. 27.02.2011), , 1, 3, , (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 171. ABC is an isosceles right angled, triangle with ÐB = 90°. On the, sides AC and AB, two equilateral, triangles ACD and ABE have, been constructed. The ratio of, area of DABE and DACD is, (1) 1 : 3, (2) 2 : 3, (3) 1 : 2, , (4) 1 :, , 2, , (SSC CHSL DEO & LDC Exam., 27.10.2013 IInd Sitting), , 172. Two triangles ABC and DEF are, similar to each other in which AB, = 10 cm, DE = 8 cm. Then the, ratio of the area of triangles ABC, and DEF is, (1) 4 : 5, (2) 25 : 16, (3) 64 : 125, (4) 4 : 7, (SSC CHSL DEO & LDC Exam., 04.11.2012, IInd Sitting), , 173. If DABC is similar to DDEF such, that BC = 3 cm, EF = 4 cm and, area of DABC = 54 cm2, then the, area of DDEF is :, (1) 66 cm2, (2) 78 cm2, (3) 96 cm2, (4) 54 cm2, (SSC Graduate Level Tier-I, Exam. 21.04.2013, Ist Sitting), , 174. The area of two similar triangles, ABC and DEF are 20 cm2 and 45, cm2 respectively. If AB = 5 cm,, then DE is equal to :, (1) 6.5 cm, (2) 7.5 cm, (3) 8.5 cm, (4) 5.5 cm, (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 175. ABCD is a parallelogram. BC is, produced to Q such that BC =, CQ. Then, (1) area (D BCP) = area (D DPQ), (2) area (D BCP) > area (D DPQ), (3) area (D BCP) < area (D DPQ), (4) area (D BCP) + area (D DPQ), = area (DBCD), (SSC Graduate Level Tier-I, Exam. 21.04.2013 IInd Sitting), , 176. The ratio of the length of the, parallel sides of a trapezium is, 3:2. The shortest distance, between them is 15 cm. If the, area of the trapezium is 450 cm2,, the sum of the length of the, parallel sides is, , SME–1123, , (2) 36 cm, (4) 60 cm, , 177. C1 and C 2 are two concentric, circles with centre at O. Their, radii are 12 cm. and 3 cm. respectively. B and C are the point, of contact of two tangents drawn, to C2 from a point A lying on the, circle C1. Then, the area of the, quadrilateral ABOC is, (1), , 9 15, sq. cm., 2, , (2) 12 15 sq. cm., (3) 9 15 sq. cm., (4) 6 15 sq. cm., (SSC Graduate Level Tier-I, Exam. 21.04.2013 IInd Sitting), , 178. From a point P which is at a, distance of 13 cm from centre O, of a circle of radius 5 cm, in the, same plane, a pair of tangents PQ, and PR are drawn to the circle., Area of quadrilateral PQOR is, (1) 65 cm2, (2) 60 cm2, (3) 30 cm2, (4) 90 cm2, (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 179. In D ABC, O is the centroid and, AD, BE, CF are three medians, and the area of D AOE = 15 cm2,, then area of quadrilateral, BDOF is, (1) 20 cm2, (2) 30 cm2, 2, (3) 40 cm, (4) 25 cm2, (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (North Zone), , 180. A straight line parallel to the base, BC of the triangle ABC intersects, AB and AC at the points D and E, respectively. If the area of the, DABE be 36 sq.cm, then the area, of the DACD is, (1) 18 sq.cm, (2) 36 sq.cm, (3) 18 cm, (4) 36 cm, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (North Zone), , 181. If in a D ABC, the medians CD, and BE intersect each other at, 0, then the ratio of the areas of D, ODE and D ABC is, (1) 1 : 6, (2) 6 : 1, (3) 1 : 12, (4) l2 : 1, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (East Zone)

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MENSURATION, 182.Three circles of radii 4 cm, 6 cm, and 8 cm touch each other pairwise externally. The area of the, triangle formed, by the line-segments joining-the centres of the, three circles is, (1) 144, (2) 12, , 13 sq. cm, , 187. The difference between the radii, of the bigger circle and smaller, circle is 14 cm and the difference between their areas is 1056, cm 2 . Radi us of the smaller, circle is, (1) 7 cm, (2) 5 cm, (3) 9 cm, (4) 3 cm, (SSC CGL Tier-I Re-Exam. (2013), , 105 sq. cm, , (3) 6 6 sq. cm, (4) 24 6 sq. cm, (SSC CHSL DEO & LDC Exam., 21.10.2012 (Ist Sitting), , 183. Two circles with centre A and B, and radius 2 units touch each, other externally at ‘C’. A third circle with centre ‘C’ and radius ‘2’, units meets other two at D and, E. Then the area of the quadrilateral ABDE is, (1) 2 2 sq. units, (2) 3 3 sq. units, (3) 3 2 sq. units, (4) 2 3 sq. units, (SSC CHSL DEO & LDC Exam., 04.11.2012 (IInd Sitting), , 184. ABC is a right angled triangle, B, being the right angle. Mid-points, of BC and AC are respectively B¢, and A¢. The ratio of the area of, the quadrilateral AA¢ B¢B to the, area of the triangle ABC is, (1) 1 : 2, (2) 2 : 3, (3) 3 : 4, (4) None of the above, (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 185. Two triangles ABC and PQR are, congruent. If the area of D ABC, is 60 sq. cm, then area of D PQR, will be, (1) 60 sq.cm, (2) 30 sq.cm, (3) 15 sq.cm, (4) 120 sq.cm, (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , 186. In DPQR, the line drawn from the, vertex P intersects QR at a point, S. If QR = 4.5 cm and SR = 1.5, cm then the ratios of the area of, triangle PQS and triangle PSR is, (1) 4 : 1, (3) 3 : 2, , (2) 3 : 1, (4) 2 : 1, , (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , 20.07.2014 (Ist Sitting), , 188. ABCD is parallelogram. P and Q, are the mid-points of sides BC, and CD respectively. If the area, of D ABC is 12 cm2, then the area, of D APQ is, (1) 12 cm2, (2) 8 cm2, 2, (3) 9 cm, (4) 10 cm2, (SSC CGL Tier-I Re-Exam. (2013), , 193. If the lengths of the sides AB,, BC and CA of a triangle ABC are, 10 cm, 8 cm and 6 cm respectively and if M is the mid - point, of BC and MN || AB to cut AC at, N, then the area of the trapezium ABMN is equal to, (1) 18 sq. cm. (2) 20 sq. cm., (3) 12 sq. cm. (4) 16 sq. cm., 194. ABCD is a trapezium with AD, and BC parallel sides. E is a point, on BC. The ratio of the area of, ABCD to that of AED is, , AD, , (1), , 20.07.2014 (IInd Sitting), , 189. ABC is a right angled triangle. B, being the right angle. Mid-points, of BC and AC are respectiveely, B¢ and A¢. Area of DA¢B¢C¢ is, (1), , 1, × area of DABC, 2, , (2), , 2, × area of DABC, 3, , 1, (3), × area of DABC, 4, (4), , 1, × area of DABC, 8, (SSC CGL Tier-I Exam., 19.10.2014 (Ist Sitting), , 190. A wire of length 44 cm is first, bent to form a circle and then, rebent to form a square. The difference of the two enclosed areas is, (1) 44 cm2, (2) 33 cm2, 2, (3) 55 cm, (4) 66 cm2, (SSC CGL Tier-I Exam. 19.10.2014), , 191. A parallelogram has sides 60 m, and 40m and one of its diagonals is 80 m long. Its area is, (1) 500, , 2, 15 m, , (2) 600, , 2, 15 m, , (3) 400, , 2, 15 m, , (4) 450, , 2, 15 m, , AD + BE, , (3), , AD + CE, , BE, , (4), , EC, AD + BC, AD, , (SSC CGL Tier-II Exam. 21.09.2014), , 195. In an equilateral triangle of side, 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is, , e, , j, , 3 = 1732, ., , (1) 98.55 sq cm (2) 100 sq cm, (3) 101 sq cm, , (4) 95 sq cm, , (SSC CGL Tier-II Exam. 21.0.2014), , 196. Perimeter of a rhombus is 2p, unit and sum of length of diagonals is m unit, then area of the, rhombus is, (1), , 1 2, m p sq unit, 4, , (2) 1 mp 2 sq unit, 4, (3), (4), , 1, m 2 - p 2 sq unit, 4, , e, , j, , 1 2, p - m 2 sq unit, 4, , e, , j, , (SSC CGL Tier-II Exam. 21.09.2014), , (SSC CGL Tier-I Exam. 26.10.2014), , 192. ÐACB is an angle in the semicircle of diameter AB = 5 and AC :, BC = 3 : 4. The area of the triangle ABC is, (1) 6 2 sq. cm (2) 4 sq. cm, (3) 12 sq. cm, , (2), , BC, , (4) 6 sq. cm, , (SSC CGL Tier-I Exam. 26.10.2014), , SME–1124, , 197. Two sides of a plot measuring, 32 m and 24 m and the angle, between them is a perfect right, angle. The other two sides measure 25 m each and the other, three angles are not right angles., The area of the plot in m2 is, (1) 768, , (2) 534, , (3) 696.5, , (4) 684, , (SSC CGL Tier-II Exam. 21.09.2014)

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MENSURATION, 198. a and b are two sides adjacent, to the right angle of a right-angled triangle and p is the perpendicular drawn to the hypotenuse from the opposite vertex., Then p2 is equal to, (1) a2 + b2, (3), , a 2b 2, a 2 + b2, , (2), , 1, a2, , +, , 1, b2, , (4) a2 – b2, , (SSC CGL Tier-II Exam. 21.09.2014), , 199. A is the centre of circle whose, radius is 8 and B is the centre, of a circle whose diameter is 8., If these two circles touch externally, then the area of the circle, with diameter AB is, (1) 36 p, (2) 64 p, (3) 144 p, (4) 256 p, , 204. If the numerical value of the circumference and area of a circle, is same, then the area is, (1) 6 p sq. unit (2) 4 p sq. unit, (3) 8 p sq. unit (4) 12 p sq. unit, , 209. The sides of a rhombus are 10, cm each and a diagonal measures, 16 cm. Area of the rhombus is, (1) 96 sq.cm, (2) 160 sq.cm, (3) 100 sq. cm (4) 40 sq.cm, , (SSC CHSL DEO & LDC Exam., , (SSC CHSL DEO Exam. 02.11.2014, , 02.11.2014 (IInd Sitting), , 205. The area of an equilateral triangle is 48 sq. cm. The length of, the side is, (1), , 8 × 4 cm (2) 4 3 cm, , (3) 8 cm, , 02.11.2014 (IInd Sitting), , 206. Area of regular hexagon with side, ‘a’ is, (1), , 3 3 2, a sq. unit, 4, , (SSC CGL Tier-II Exam. 21.09.2014), , 200. The length of a rectangle is increased by 10% and breadth decreased by 10%. The area of the, new rectangle is, (1) neither increased nor decreased, (2) increased by 1%, (3) decreased by 2%, (4) decreased by 1%, , (4) 16 cm, , (SSC CHSL DEO & LDC Exam., , (2), , (3), , 12, , a2 sq. unit, , 2 3, , 2, , 201. If the numerical values of the, height and the area of an equilateral triangle be same, then the, length of each side of the triangle is, (1) 2 units, (2) 4 units, (3) 5 units, (4) 8 units, , (SSC CHSL DEO & LDC, Exam. 9.11.2014), , 207. The external fencing of a circular, path around a circular plot of land, is 33 m more than its interior, fencing. The width of the path, around the plot is, (1) 5.52 m, (2) 5.25 m, (3) 2.55 m, (4) 2.25 m, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014), , 202. If the length of a side of the square, is equal to that of the diameter of, a circle, then the ratio of the area, of the square and that of the circle is, , FG p = 22 IJ, H 7K, , (1) 14 : 11, (3) 11 : 14, , (2) 7 : 11, (4) 11 : 7, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014), , 203. The median of an equilateral tri-, , the area of trapezium DECB, the area of DABC, , (SSC CHSL DEO & LDC Exam., 02.11.2014 (IInd Sitting), , AD, =, BD, , (2), , 4, 5, , (4) 160, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , is, , 21, 25, , (4) 5, , 1, 4, , (SSC CHSL DEO & LDC, Exam. 9.11.2014), , SME–1125, , TF No. 022 MH 3), , 214. If the ratio of the altitudes of two, triangles be 3 : 4 and the ratio of, their corresponding areas be 4 :, 3, then the ratio of their corresponding lengths of bases is, (1) 1 : 1, (2) 16 : 9, (3) 1 : 2, (4) 2 : 1, (SSC CHSL (10+2) DEO & LDC, , equal to, , (3) 1, , (4) 36 3, , (3) 120, , (SSC CGL Tier-I Exam. 19.10.2014, , 2, . Then, 3, , (3) 72 3, , (Ist Sitting), , 211. The lengths of two parallel sides, of a trapezium are 6 cm and 8, cm. If the height of the trapezium be 4 cm, then its area is, (1) 28 cm, (2) 28 sq.cm, (3) 30 sq.cm, (4) 30 cm, , Exam. 9.11.2014), , tively so that DE||BC and, , 5, 9, , (SSC CHSL DEO Exam. 16.11.2014, , (SSC CHSL DEO & LDC, , on the sides AB and AC respec-, , (1), , (4) 25 m2, , 213. A wire is bent into the form of a, circle, whose area is 154 cm2. If, the same wire is bent into the form, of an equilateral triangle, the approximate area of the equilateral, triangle is, (1) 93.14 cm2 (2) 90.14 cm2, (3) 83.14 cm2 (4) 39.14 cm2, , 208. In D ABC, D and E are two points, , angle is 6 3 cm. The area (in, cm2) of the triangle is, (1) 72, (2) 108, , (3) 27 2 m2, , 212. If a and b are the lengths of the, sides of a right triangle whose, hypotenuse is 10 and whose area, is 20, then the value of (a + b)2 is, (1) 140, (2) 180, , a2 sq. unit, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014), , (2) 54 6 m2, , (SSC CHSL DEO Exam. 16.11.2014, , a2 sq. unit, , 2 3, 6, , (1) 18 m2, , (Ist Sitting), , 9, , (4), , (Ist Sitting), , 210. The perimeter of a triangle is 54, m and its sides are in the ratio of, 5 : 6 : 7. The area of the triangle is, , Exam. 16.11.2014 , Ist Sitting, TF No. 333 LO 2), , 215. Let A be the area of a square, whose each side is 10 cm. Let B, be the area of a square whose, diagonals are 14 cm each. Then, (A – B) is equal to, (1) 0, (2) 1, (3) 2, (4) 4, (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014 , Ist Sitting, TF No. 333 LO 2)

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MENSURATION, 216. Two sides of a parallelogram are, 20 cm and 25 cm. If the altitude, corresponding to the side of, length 25 cm is 10 cm, then the, altitude corresponding to the other pair of sides is, (1) 10.5 cm, (2) 12 cm, (3) 12.5 cm, (4) 10 cm, , 221. The outer and inner diameter of, a circular path be 728 metre and, 70 0 metre respectively. T he, breadth of the path is, (1) 7 metre, (2) 28 metre, , (SSC CHSL (10+2) DEO & LDC, , 222. The area of the parallelogram, whose length is 30 cm, width is, 20 cm and one diagonal is 40, cm is, , Exam. 16.11.2014 , Ist Sitting, TF No. 333 LO 2), , 217. If the sides of an equilateral triangle be increased by 1 m its area, is increased by 3 sq. metre., The length of any of its sides is, (1) 2 metre, , 3, metre, (3), 2, , (2), , (4), , 5, metre, 2, , 3 metre, , (SSC CHSL (10+2) DEO & LDC, Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , 218. The in-radius of a triangle is 6, cm, and the sum of the lengths, of its sides is 50 cm. The area of, the triangle (in square cm.) is, (1) 150, (2) 50, (3) 300, , (4) 56, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 219. One of the angles of a right-angled triangle is 15°, and the hypotenuse is 1 metre. The area of, the triangle (in square cm.) is, (1) 1220, (2) 1200, (3) 1250, , (4) 1215, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 220. If for an isosceles triangle the, length of each equal side is ‘a’, units and that of the third side is, ‘b’ units, then its area will be, (1), , a, 4b2 – a 2 square units, 4, , a, 2a 2 – b2 square units, (2), 2, (3), , (4), , b, 4a 2 – b2 square units, 4, b, a 2 – 2b2 square units, 2, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , (3) 14 metre, , (4) 20 metre, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 2, 15 cm, , (1) 200, (2) 100, , 2, 15 cm, , (3) 300, , 2, 15 cm, , (4) 150, , 2, 15 cm, , TF No. 567 TL 9), , (4) 68 square cm., (SSC CGL Tier-II Exam. 12.04.2015, , (1) 20 2 square cm., (2) 12 2 square cm., (3) 25 2 square cm., (4) 15 2 square cm., (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , (4) 9 : 4, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 224. The area of a circle is 324 p, square cm. The length of its longest chord (in cm.) is, (1) 36, (2) 28, (4) 32, , 229. The length of the diagonal of a, rectangle with sides 4 m and 3, m would be, (1) 12 m, (2) 7 m, (3) 5 m, , TF No. 567 TL 9), , 225. The area of a rhombus is 256, square cm. and one of its diagonals is twice the other in length., Then length of i ts l arger, diagonal is, (1) 32 cm, (2) 16 cm, (4) 24 cm, , (SSC CGL Tier-II Exam. 12.04.2015, , 230. In a right angled triangle DPQR,, PR is the hypotenuse of length, 20 cm, ÐPRQ = 30°, the area of, the triangle is, (1) 50 3 cm2, , (2) 100 3 cm2, , (3) 25 3 cm2, , (4), , 1, 2, , (x + 1) units and its diagonal is, , 3–x, 2, , units, then the length of, , the side of the square would be, (1), , 4, units, 3, , (3) 1 unit, , (2), , 1, unit, 2, , (4) 2 units, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , SME–1126, , 100, 3, , cm2, , (SSC CGL Tier-II Exam. 12.04.2015, , TF No. 567 TL 9), , 226. If the side of a square is, , (4) 14 m, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , (SSC CGL Tier-II Exam. 12.04.2015, , (3) 48 cm, , (1) 56 square cm., (2) 84 square cm., (3) 48 square cm., , TF No. 567 TL 9), , 223. On increasing each side of a, square by 50%, the ratio of the, area of new square formed and, the given square will be, (1) 9 : 5, (2) 9 : 3.5, , (3) 38, , 22, ), 7, , 228. If the length of each of two equal, sides of an isosceles triangle is, 10 cm. and the adjacent angle is, 45°, then the area of the triangle is, , (SSC CGL Tier-II Exam. 12.04.2015, , (3) 9 : 7, , 227. The circumference of a triangle, is 24 cm and the circumference, of its in-circle is 44 cm. Then the, area of the triangle is (taking p =, , TF No. 567 TL 9), , 231. The perimeter of an equilateral triangle is equal to the circumference of a circle. The ratio of their, areas is, , FG Use p = 22 IJ, H, 7 K, (1) 22 : 21 3, , (2) 21 : 22 3, , (3) 21 : 22 2, , (4) 22 : 21 2, , (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7)

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MENSURATION, 232. From any point inside an equilateral triangle, the lengths of perpendiculars on the sides are ‘a’, cm, ‘b’ cm and ‘c’ cms. Its area, (in cm2) is, , 2, (a + b + c), 3, , (1), , 237. The diagonal of a quadrilateral, shaped field is 24m and the perpendiculars dropped on it from, the remaining opposite vertices, are 8m and 13m. The area of the, field is, (1) 252 m2, (2) 156 m2, (3) 96 m2, (4) 1152 m2, , 3, (2), (a + b + c)2, 3, (3), , 3, (a + b + c), 3, , (4), , 2, (a + b + c)2, 3, , (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 233. The areas of a circle and a square, are same. The ratio of the side of, the square to the radius of the, circle is, (1) 2p : 1, (3), , (2) 1 :, , p, , (4) 1 : p, , p :1, , (SSC CGL Tier-II Exam,, , 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 234. ABCD is a square inscribed in a, circle of radius r. Then the total, area (in square units) of the portions of the circle lying outside, the square is, (1) p (r2 – 4), (2) 2p (r2 – 1), (3) p2 r (r – 7), (4) r2 (p – 2), (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 235. The lengths of the two parallel, sides of a trapezium are 28 cm, and 40 cm. If the length of each, of its other two sides be 12 cm,, then the area (in cm2) of the trapezium is, (1) 312 5, (3) 204 3, , 243. Two circles touch each other externally. The sum of their areas, is 130 p sq cm and the distance, between their centres is 14 cm., The radius of the smaller circle is, (1) 2 cm, (2) 4 cm, (3) 5 cm, (4) 3 cm, (SSC CGL Tier-I Exam, 09.08.2015, , (SSC CAPFs SI, CISF ASI & Delhi, , (IInd Sitting) TF No. 4239378), , Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 244. Let C1 and C2 be the inscribed, and circumscribed circles of a, triangle with sides 3cm, 4cm and, , 238. Two isosceles triangles have equal, vertical angles and their areas are, in the ratio 9:16. Then the ratio, of their corresponding heights is(1) 4.5 : 8, (2) 4 : 3, (3) 8 : 4.5, (4) 3 : 4, , area of C1, 5cm then area of C is, 2, (1), , 9, 25, , (2), , 4, 25, , (3), , 9, 16, , (4), , 16, 25, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 239. In DABC, a line through A cuts, the side BC at D such that BD :, DC = 4 : 5. If the area of DABD, = 60 cm 2 , then the area of, DADC is, (1) 90 cm2, (2) 50 cm2, 2, (3) 60 cm, (4) 75 cm2, (SSC CGL Tier-I Exam, 09.08.2015, (Ist Sitting) TF No. 1443088), , 240. If the area of a circle is A, radius, of the circle is r and circumference of it is C, then, , A, =C, (1), r, (3), , C r, =, A, 2, , (2) rC = 2A, , (4) AC =, , r2, 4, , (SSC CGL Tier-I Exam, 09.08.2015, (Ist Sitting) TF No. 1443088), , 241. In a rhombus ABCD, ÐA = 60°, and AB = 12 cm. Then the diagonal BD is, , (2) 408 3, , (1) 10 cm, , (2) 2 3 cm, , (4) 504 3, , (3) 6 cm, , (4) 12 cm, , (SSC CGL Tier-I Exam, 16.08.2015, (Ist Sitting) TF No. 3196279), , 245. If the altitude of an equilateral, triangle is 12 3 cm, then its, area would be :, (1) 12 cm2, , (2) 144, , (3) 72 cm2, , (4) 36, , 2, 3 cm, 2, 3 cm, , (SSC CGL Tier-I Exam, 16.08.2015, (Ist Sitting) TF No. 3196279), , 246. Given that : DABC ~ DPQR, If, , area (DPQR) 256, =, and PR = 12, area (DABC) 441, cm, then AC is equal to, (1) 15.75 cm (2) 16 cm, (3) 12 2 cm (4) 15.5 cm, (SSC CGL Tier-I Exam, 16.08.2015, (IInd Sitting) TF No. 2176783), , 247. ABCD is a cyclic quadrilateral., Diagonals AC and BD meets at P., If ÐAPB = 110° and ÐCBD = 30°,, then ÐADB measures, (1) 55°, (2) 30°, (3) 70°, (4) 80°, (SSC CGL Tier-I Exam, 16.08.2015, , (SSC CGL Tier-II Exam,, , (SSC CGL Tier-I Exam, 09.08.2015, , (IInd Sitting) TF No. 2176783), , (IInd Sitting) TF No. 4239378), , 236. The perimeter of a sheet of paper in the shape of a quadrant of, a circle is 75 cm. Its area would, , 242. If two medians BE and CF of a, triangle ABC, intersect each other at G and if BG = CG, ÐBGC =, 60° and BC = 8 cm then area of, the triangle ABC is, , 248. A circular swimming pool is surrounded by a concrete wall 4m, wide. If the area of the concrete, , 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , FG, H, , be p =, , 22, 7, , IJ, K, , (1) 100 cm2, (3) 693 cm2, , (2) 346.5 cm2, (4) 512.25 cm2, , (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 2, (1) 96 3 cm (2) 64 3 cm2, , (3) 48 3 cm2 (4) 48 cm2, (SSC CGL Tier-I Exam, 09.08.2015, (IInd Sitting) TF No. 4239378), , SME–1127, , wall surrounding the pool is, , 11, 25, , that of the pool, then the radius, (in m) of the pool is :, (1) 8, (2) 16, (3) 30, (4) 20, (SSC CGL Tier-I Exam, 16.08.2015, (IInd Sitting) TF No. 2176783)

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MENSURATION, 249. D ABC is similar to D DEF. The ratio, of their perimeters is 4 : 1. The, ratio of their areas is, (1) 4 : 1, (2) 16 : 1, (4) 8 2 : 1, , (3) 8 : 1, , (SSC CGL Tier-I, Re-Exam, 30.08.2015), , 250. The amount of rice produced in, a square field of side 50 m is 750, kg. The amount of rice produced, in a similar square field of side, 100 m will be, (1) 2000 kg, (2) 3000 kg, (3) 3500 kg, (4) 1500 kg, (SSC Constable (GD), Exam, 04.10.2015, IInd Sitting), , 251. The time required for a boy to, travel along the external and, internal boundaries of a circular, path are in the ratio 20 : 19. If, the width of the path be 5 metres,, the internal diameter is :, (1) 195 metres (2) 192 metres, (3) 180 metres (4) 190 metres, (SSC Constable (GD), Exam, 04.10.2015, IInd Sitting), , 252. In triangle ABC, DE || BC where, D is a point on AB and E is a, point on AC. DE divides the area, of D ABC into two equal parts., Then DB : AB is equal to, , e, : e, , (1), , 2 :, , (2), , 2, , (3), (4), , e, e, , j, 2 – 1j, 2 +1, , j, 2 + 1j :, 2 –1 :, , 2, 2, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 253. The centroid of a D ABC is G. The, area of D ABC is 60 cm2. The area, of DGBC is, (1) 10 cm2, (2) 30 cm2, (3) 40 cm2, , (4) 20 cm2, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 254. In trapezium ABCD, AB ||CD and, AB = 2CD. Its diagonals intersect, at O. If the area of DAOB = 84, cm2, then the area of DCOD is, equal to, (1) 72 cm2 (2) 21 cm2, (3) 42 cm2 (4), 26 cm2, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 255. Given that the ratio of altitudes of, two triangles is 4 : 5, ratio of their, areas is 3 : 2. The ratio of their, corresponding bases is, , (1) 8 : 15, (3) 5 : 8, , (2) 15 : 8, (4) 8 : 5, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 256. The area of an isosceles trapezium, is 176 cm2 and the height is, , (2), , (3) 2 137, , 1, 2, , (2), , 2, 1, , (3), , 1, 3, , (4), , 2, 3, , (SSC CHSL (10+2) LDC, DEO, , 2, th, 11, , of the sum of its parallel sides. If, the ratio of the length of the, parallel sides is 4 : 7, then the, length of a diagonal (in cm) is, (1) 28, , (1), , 137, , (4) 24, , & PA/SA Exam, 06.12.2015, (IInd Sitting) TF No. 3441135), , 262. The hypotenuse of a right–angled, triangle is 39 cm and the, difference of other two sides is, 21 cm. Then, the area of the, triangle is, (1) 270 sq. cm (2) 450 sq. cm, (3) 540 sq. cm (4) 180 sq. cm, (SSC CHSL (10+2) LDC, DEO, , (SSC CGL Tier-II Exam,, , & PA/SA Exam, 20.12.2015, (Ist Sitting) TF No. 9692918), , 25.10.2015, TF No. 1099685), , 257. The area of a circle whose radius, is the diagonal of a square whose, area is 4 sq. units is :, (1) 16p sq. units (2) 4p sq. units, (3) 6p sq. units (4) 8p sq. units, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (Ist Sitting) TF No. 6636838), , 258. A rectangular carpet has an area, of 120 m2 and a perimeter of 46, metre. The length of its diagonal, is :, (1) 23 metre, (2) 13 metre, (3) 17 metre, (4) 21 metre, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (Ist Sitting) TF No. 6636838), , 259. A plate on square base made of, brass is of length x cm and width, 1 mm. The plate weighs 4725, gm. If 1 cubic cm of brass weighs, 8.4 gram, then the value of x is :, (1) 75, (2) 76, (3) 72, (4) 74, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (IInd Sitting) TF No. 7203752), , 260. The length of two parallel sides, of a trapezium are 15 cm and 20, cm. If its area is 175 sq.cm, then, its height is :, (1) 15 cm, (2) 10 cm, (3) 20 cm, (4) 25 cm, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (IInd Sitting) TF No. 3441135), , 261. ABCD is a square. Draw a triangle QBC on side BC considering, BC as base and draw a triangle, PAC on AC as its base such that, ~ D PAC., D QBC, Then,, , Area of DQBC, is equal to :, Area of DPAC, , SME–1128, , 263. The ratio between the length and, the breadth of a rectangular park, is 3 : 2. If a man cycling along, the boundary of the park at the, speed of 12 km/hour completes, one round in 8 minutes, then the, area of the park is, (1) 153650 sq.metre, (2) 135600 sq.metre, (3) 153600 sq.metre, (4) 156300 sq.metre, (SSC CGL Tier-II Online, Exam.01.12.2016), , 264. A rectangular park 60 metre long, and 40 metre wide has two concrete crossroads running in the, middle of the park and rest of, the park has been used as a, lawn. If the area of the lawn is, 2109 metre2 then the width of the, road is, (1) 3 metre, (2) 5 metre, (3) 6 metre, (4) 2 metre, (SSC CGL Tier-II Online, Exam.01.12.2016), , 265. A square and a regular hexagon, are drawn such that all the vertices of the square and the hexagon are on a circle of radius r cm., The ratio of area of the square, and the hexagon is, (1) 3 : 4, (3), , 2 :, , (2) 4 : 3 3, , 3, , (4) 1 :, , 2, , (SSC CGL Tier-II Online, Exam.01.12.2016), , 266. DABC is similar to DDEF. If the, area of DABC is 9 sq.cm. and the, area of DDEF is 16 sq.cm. and, BC = 2.1 cm, then the length of, EF will be, (1) 5.6 cm., (2) 2.8 cm., (3) 3.7 cm., (4) 1.4 cm., (SSC CGL Tier-II Online, Exam.01.12.2016)

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MENSURATION, 267. If D and E are the mid-points of, AB and AC respectively of DABC,, then the ratio of the areas of D, ADE and, BCED is, (1) 1 : 2, (2) 1 : 4, (3) 2 : 3, (4) 1 : 3, , 272. Area of the circle inscribed in a, square of diagonal 6 2 cm. (in, sq. cm.) is, (1) 9 p, (2) 6 p, , (SSC CGL Tier-II Online, Exam.01.12.2016), , (SSC CGL Tier-I (CBE), Exam. 09.09.2016) (Ist Sitting), , 268. What is the area of dark (coloured) sector for the figure given below?, , 273. The diagonals of two squares are, in the ratio 5 : 2. The ratio of, their area is, (1) 5 : 6, (2) 25 : 4, (3) 5 : 4, (4) 125 : 8, , (3) 3 p, , (4) 9 2 p, , (SSC CGL Tier-I (CBE), Exam. 09.09.2016) (Ist Sitting), , 4 cm., , 0, , 120°, , B, , 274. In D ABC and D PQR, Ð B, = Ð Q, ÐC = ÐR. M is the midpoint of side QR. If AB : PQ = 7 :, 4, then, , (1), , 1, 2, , (2) 1, , (3), , 1, 3, , (4), , A, , (2) 25.28, (4) 18.56, , 278. If D, E and F are the mid–points, of the sides of an equilateral triangle ABC, then the ratio of the area, of triangle DEF and DCF is :, , A, , E, , A, , P, , B, , (SSC CPO SI, ASI Online, Exam.05.06.2016) (IInd Sitting), , 269. If two medians BE and CF of a, triangle ABC, intersect each other, at G and if BG = CG, angle BGC, = 120°, BC = 10 cm, then area of, the triangle ABC is :, (1) 50 3 cm2 (2) 60 cm2, (4) 25 3 cm2, , (3) 25 cm2, , (SSC CPO SI, ASI Online, Exam.05.06.2016) (IInd Sitting), , 270. A room 16m 5cm long and 15 m, broad is to be fitted with equal, square tiles. How many number, of largest possible tiles are required so that they exactly fit?, (1) 10400, (3) 10800, , (2) 10700, (4) 9800, , (SSC CPO SI, ASI Online, Exam.05.06.2016) (IInd Sitting), , 35, (1), 8, (3), , 49, 8, , Q, , M, , R, , 49, (2), 16, (4), , 35, 16, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , 275. The diagonals of two squares are, in the ratio of 3 : 7. What is the, ratio of their areas?, (1) 3 : 7, (2) 9 : 49, (3) 4 : 7, (4) 7 : 3, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , 2, , 276. A string of length 24 cm is bent, first into a square and then into, a right–angled triangle by keeping one side of the square fixed, as its base. Then the area of triangle equals to :, (1) 24 cm2, (2) 60 cm2, (3) 40 cm2, (4) 28 cm2, , 2, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , 271. Three equal circles of unit radius, touch one another. Then the area, of the circle circumscribing the, three circles is, 2, , e, j, p, e2 + 3 j, 6, , (1) 6 p 2 + 3, , p, 2+ 3, (3), 3, , e, , j, , e, , j, , (4) 3p 2 + 3, , C, , B, , 2, , (SSC CPO Exam. 06.06.2016), (Ist Sitting), , 277. ABCD is a square. Draw an equilateral triangle PBC on side BC, considering BC is a base and an, equilateral triangle QAC on diagonal AC considering AC is a base., Find the value of, , SME–1129, , 1, 4, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , area( DABC), is :, area(DPMR), , (1) 8.38, (3) 16.76, , (2), , Area of DPBC, ., Area of DQAC, , (1) 1.1 : 1, (3) 0.9 : 1, , F, , D, , C, (2) 1 : 1.1, (4) 1 : 1, , (SSC CGL Tier-I (CBE), Exam. 27.08.2016) (IInd Sitting), , 279. The area of a rectangle is 60 cm2, and its perimeter is 34 cm, then, the length of the diagonal is, (1) 17 cm, (2) 11 cm, (3) 15 cm, (4) 13 cm, (SSC CGL Tier-I (CBE), Exam. 29.08.2016) (IInd Sitting), , 280. The centroid of a triangle DABC, is G. If the area of D ABC = 72, sq. units , then the area of D BGC, is, (1) 16 sq. units (2) 24 sq. units, (3) 36 sq. units (4) 48 sq. units, (SSC CGL Tier-I (CBE), Exam. 30.08.2016) (Ist Sitting), , 281. In a trapezium ABCD, AB || CD,, AB < CD, CD = 6 cm and distance between the parallel sides, is 4 cm. If the area of ABCD is, 16 cm2, then AB is, (1) 1 cm, (2) 2 cm, (3) 3 cm, (4) 8 cm, (SSC CGL Tier-I (CBE), Exam. 31.08.2016) (Ist Sitting), , 282. In a triangle ABC, AB = 8 cm, AC, = 10 cm and ÐB = 90°, then the, area of DABC is, (1) 49 sq.cm (2) 36 sq.cm, (3) 25 sq.cm (4) 24 sq.cm, (SSC CGL Tier-I (CBE), Exam. 01.09.2016) (Ist Sitting)

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MENSURATION, 283. In figure, DE || BC. If DE = 3, cm, BC = 6 cm and area of DADE, = 15 sq. cm, then the area of, DABC is, , A, , D, , B, , (SSC CGL Tier-I (CBE), Exam. 30.08.2016) (IInd Sitting), , 290. A rectangle with one side 4 cm is, inscribed in a circle of radius 2.5, cm. The area of the rectangle is :, (1) 8 cm2, (2) 12 cm2, 2, (3) 16 cm, (4) 20 cm2, , E, , C, , (1) 75 sq. cm., (3) 30 sq. cm., , 289. A rectangle with one side of length, 4 cm. is inscribed in a circle of, diameter 5 cm. Find, the area of, the rectangle., (1) 21 cm.2, (2) 12 cm.2, (3) 4 cm.2, (4) 3 cm.2, , (2) 45 sq. cm., (4) 60 sq. cm., , (SSC CGL Tier-I (CBE), Exam. 02.09.2016) (Ist Sitting), , 284. DABC is a right angled triangle,, the radius of its circumcircle is 3, cm and the length of its altitude, drawn from the opposite vertex, to the hypotenuse is 2 cm. Then, the area of the triangle is, (1) 12 sq. cm. (2) 3 sq. cm., (3) 6 sq. cm., (4) 5 sq. cm., , (SSC CGL Tier-I (CBE), Exam. 02.09.2016) (Ist Sitting), , 285. The lengths of the diagonals of a, rhombus are 8 cm and 6 cm. The, area of rhombus is :, (1) 96 cm2, (2) 60 cm2, 2, (3) 48 cm, (4) 24 cm2, (SSC CGL Tier-I (CBE), Exam. 06.09.2016) (Ist Sitting), , 286. Two adjacent sides of a parallelogram are 21 cms and 20 cms., The diagonal joining the end, points of these two sides is 29, cms. The area of the parallelogram (in sq. cms) is, (1) 240, (2) 120, (3) 210, (4) 420, (SSC CGL Tier-I (CBE), Exam. 07.09.2016) (Ist Sitting), , 287. D ABC is an equilateral triangle, and D and E are midpoints of AB, and BC respectively. Then the, area of D ABC : the area of the, trapezium ADEC is, (1) 5 : 3, (2) 4 : 1, (3) 8 : 5, (4) 4 : 3, (SSC CGL Tier-I (CBE), Exam. 07.09.2016) (Ist Sitting), , 288. The perimeters of a square and a, rectangle are equal . If their area, be ‘A’ m2 and ‘B’ m2 respectively,, then correct statement is, (1) A < B, (2) A < B, (3) A > B, (4) A > B, (SSC CGL Tier-I (CBE), Exam. 30.08.2016) (IInd Sitting), , (SSC CGL Tier-I (CBE), Exam. 31.08.2016) (IInd Sitting), , 291. If O is the centroid and AD, BE, and CF are the three medians of, DABC with an area of 96 cm2 then, the area of DBOD in cm2 is, (1) 8, (2) 12, (3) 16, (4) 24, (SSC CGL Tier-I (CBE), Exam. 01.09.2016) (IInd Sitting), , 292. DABC is similar to DDEF. If the, ratio of similar sides is k : 1, the, ratio of their areas is, (1) k2 : 1, (2) 2k : 1, (3), , k2, :1, 2, , (4) 2k2 : 1, , (SSC CGL Tier-I (CBE), Exam. 02.09.2016) (IInd Sitting), , 293. The height of an equilateral triangle is 18 cm. Its area is, (1) 36 3 square metre, (2) 108 3 square cm., (3) 108 square cm., (4) 96 3 square metre, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 294. The length and breadth of a rectangular piece of a land are in a, ratio 5 : 3. The owner spent Rs., 6000 for surrounding it from all, sides at Rs. 7.50 per metre. The, difference between its length and, breadth is, (1) 50 metre, (2) 100 metre, (3) 150 metre, (4) 250 metre, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 295. The ratio between the area of a, square and that of a circle, when, the length of a side of the square, is equal to that of the diameter of, the circle, is, , FG Take, p = 22 IJ, H, 7 K, , (1) 14 : 11, (3) 7 : 22, , (2) 28 : 11, (4) 22 : 7, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , SME–1130, , 296. A piece of wire 132 cm. long is, bent successively in the shape of, an equilateral triangle, a square, and a circle. Then area will be, longest in shape of, (1) Circle, (2) Equilateral triangle, (3) Square, (4) Equal in all the shapes, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 297. Let DABC and DABD be on the, same base AB and between the, same parallels AB and CD. Then, the relation between areas of triangles ABC and ABD will be, , 1, DABC, 3, 1, (2) DABD = DABC, 2, , (1) DABD =, , 1, DABD, 2, (4) DABC = DABD, (3) DABC =, , (SSC CGL Tier-I (CBE), Exam. 10.09.2016 (IInd Sitting), , 298. The perimeter of a rhombus is, 240 metre and the distance between any two parallel sides is, 20 metre. The area of the rhombus in square metre is, (1) 600 square metre, (2) 1200 square metre, (3) 2400 square metre, (4) 4800 square metre, (SSC CGL Tier-I (CBE), Exam. 28.08.2016 (Ist Sitting), , 299. The area of the largest triangle, that can be inscribed in a semicircle of radius 6 m is, (1) 36 m2, (2) 72 m2, 2, (3) 18 m, (4) 12 m2, (SSC CGL Tier-I (CBE), Exam. 29.08.2016 (Ist Sitting), , 300. A circle and a square have same, area. The ratio of the side of the, square to the radius of the circle, will be:, , p :1, , (1), , (3) p : 1, 2, , (2) 1 :, , p, , (4) 1 : p, , (SSC CGL Tier-I (CBE), Exam. 02.09.2016 (IInd Sitting), , 301. Point O is the centre of a circle, of radius 5 cm. At a distance of, 13 cm from O, a point P is taken. From this point, two tangents, PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is, (1) 60 cm.2, (2) 32.5 cm.2, (3) 65 cm.2, (4) 30 cm.2, , (SSC CGL Tier-I (CBE), Exam. 03.09.2016 (IIIrd Sitting)

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MENSURATION, 302. The length of a median of an equilateral triangle is 12 3 cms., Then the area of the triangle is :, (1) 144 sq. cm., , 309. O is the centre of the circle and, ÐAOB = 150°, and the shaded, portion is x part of the circular, region, then x = ?, , (2) 288 3 sq. cm., (3) 144 3 sq. cm., (4) 288 sq. cm., , A, , (SSC CGL Tier-I (CBE), Exam. 04.09.2016 (IInd Sitting), , 303. Two circles touch externally. The, sum of their areas is 130 p sq., cm. and the distance between, their centres is 14 cm. The radiu s of the bi g ger circl e i s, , FG Take p =, H, , 22, 7, , (1) 22 cm., (3) 33 cm., , IJ, K, , (SSC CGL Tier-I (CBE), Exam. 06.09.2016 (IInd Sitting), , 304. In an equilateral triangle of side, 24 cm., a circle is inscribed, touching its sides. The area of the, remaining portion of the triangle, is approximately equal to, , FG assuming p = 22 &, H, 7, (1) 36.6 cm2, (3) 72.8 cm2, , IJ, K, , 3 = 1.732, , (2) 54.2 cm2, (4) 98.5 cm2, , (SSC CGL Tier-I (CBE), Exam. 06.09.2016 (IInd Sitting), , 305. The inradius of triangle is 4 cm, and its area is 34 sq. cm. the, perimeter of the triangle is :, (1) 8.5 cm, (2) 17 cm, (3) 34 cm, (4) 20 cm, (SSC CGL Tier-I (CBE), Exam. 06.09.2016 (IIIrd Sitting), , 306. The area of a triangle ABC is 10.8, cm2. If CP = PB and 2AQ = QB,, then the area of the triangle, APQ is, (1) 3.6 cm2, (2) 0.9 cm2, (3) 2.7 cm2, (4) 1.8 cm2, (SSC CGL Tier-I (CBE), Exam. 06.09.2016 (IIIrd Sitting), , 307. If a circle of radius 12 cm is divided into two equal parts by one, concentric circle, then radius of, inner circle is :, (1) 6 cm, (2) 4 cm, (3) 6 2 cm, , (1), , 1, 12, , (2), , (4) 4 2 cm, , (SSC CGL Tier-I (CBE), Exam. 06.09.2016 (IIIrd Sitting), , 308. In DABC, the medians AD and BE, meet at G. The ratio of the areas, of DBDG and the quadrilateral, GDCE is :, (1) 1 : 2, (2) 1 : 3, (3) 2 : 3, (4) 3 : 4, , (SSC CGL Tier-I (CBE), Exam. 08.09.2016 (IInd Sitting), , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 314. In a trapezium ABCD, AB and DC, are parallel sides and Ð ADC = 90°., If AB = 15 cm, CD = 40 cm and, diagonal AC = 41 cm. then the, area of the trapezium ABCD is, (1) 245 cm.2 (2) 240 cm.2, (3) 247.5 cm.2 (4) 250 cm.2, , O, , 1, (3), 6, , (2) 11 cm., (4) 44 cm., , B, , 150°, , 313. The radii of two concentric circles are 68 cm and 22 cm. The, area of the closed figure bounded by the boundaries of the circles is, (1) 4140p sq. cm. (2) 4110p sq. cm., (3) 4080p sq. cm. (4) 4050p sq. cm., , 1, 9, , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 1, (4), 4, , (SSC CGL Tier-I (CBE), Exam. 09.09.2016 (IIIrd Sitting), , 310. The area of the circle with radius, y is w. The difference between, the areas of the bigger circle (with, radius y) and that of the smaller, , x, circle (with radius x) is w’. So, y, is equal to, , 315. The area of a rhombus having one, side 10 cm and one diagonal 12, cm is, (1) 48 cm.2, (2) 96 cm.2, (3) 144 cm.2 (4) 192 cm.2, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 316. The cost of levelling a circular field, at 50 paise per square metre is, Rs. 7700. The cost (in Rs.) of, putting up a fence all round it at, Rs. 1.20 per metre i s, , (1), , 1–, , w', w, , (2), , 1+, , w', w, , FG Use p = 22 IJ, H, 7 K, , (3), , 1+, , w, w', , (4), , 1–, , w, w', , (1) Rs. 132, (3) Rs. 528, , (SSC CGL Tier-I (CBE), Exam. 10.09.2016 (IInd Sitting), , 311. D, E and F are the mid points of, the sides BC, CA and AB respectively of a DABC. Then the ratio, of the areas of DDEF and DABC is, (1), , 1, 2, , (2), , 1, 4, , (3), , 1, 8, , (4), , 1, 16, , (SSC CGL Tier-I (CBE), Exam. 11.09.2016 (IInd Sitting), , 312. An arc AB of a circle subtends, an angle x radians at the centre, of the circle. Given that the area, of the secctor AOB is equal to the, square of the length of the arc, AB, then the value of x is :, (1), , (3), , 1, 2, 1, 3, , (2), , (4), , 1, 2, 1, 3, , (SSC CGL Tier-I (CBE), Exam. 27.10.2016 (Ist Sitting), , SME–1131, , (2) Rs. 264, (4) Rs. 1056, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 317. The sum of the l ength and, breadth of a rectangle is 6 cm. A, square is constructed such that, one of its sides is equal to a diagonal of the rectangle. If the ratio, of areas of the square and rectangle is 5 : 2, the area of the, square in cm2 is, (1) 20, (2) 10, (3) 4 5, , (4) 10 2, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 318. The length of a side of an equilateral triangle is 8 cm. The area of, the region lying between the circum circle and the incircle of the, triangle is, , FG Use : p = 22 IJ, H, 7 K, , (1) 50, , 1, cm2, 7, , (2) 50, , 2, cm2, 7, , (3) 75, , 1, cm2, 7, , (4) 75, , 2, cm2, 7, , (SSC CGL Tier-II (CBE), Exam. 12.01.2017)

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MENSURATION, 319. Two equal circles intersect so that, their centres, and the points at, which they intersect form a, square of side 1 cm. The area (in, sq.cm) of the portion that is common to the circles is, , p, 4, , (2), , p, –1, 2, , p, (3), 5, , (4), , e, , (1), , 4. The perimeter of two squares are, 40 cm and 24 cm. The perimeter, of a third square , whose area is, equal to the difference of the area, of these squares, is, (1) 34 cm, (2) 32 cm, (3) 38 cm, (4) 30 cm, (SSC CPO S.I. Exam. 09.11.2008), , j, , 2 –1, , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 320. D and E are points on the sides, AB and AC respectively of DABC, such that DE is parallel to BC and, AD : DB = 4 : 5, CD and BE intersect each other at F. Then find, the ratio of the areas of DDEF, and DCBF., (1) 16 : 25, (2) 16 : 81, (3) 81 : 16, (4) 4 : 9, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 331. Diagonals of a Trapezium ABCD, with AB || CD intersect each, other at the point O. If AB = 2CD,, then the ratio of the areas of, DAOB and DCOD is, (1) 4 : 1, (2) 1 : 16, (3) 1 : 4, (4) 16 : 1, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , TYPE–II, 1. The perimeter of two squares are, 24 cm and 32 cm. The perimeter, (in cm) of a third square equal in, area to the sum of the areas of, these squares is :, (1) 45, (2) 40, (3) 32, (4) 48, (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 5. The length and breadth of a, rectangular field are in the ratio, of 3 : 2. If the perimeter of the, field is 80m, its breadth (in, metres) is :, (1) 18, (2) 16, (3) 10, (4) 24, (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 6. The sides of a rectangular plot, are in the ratio 5:4 and its area, is equal to 500 sq.m. The perimeter of the plot is :, (1) 80m., (2) 100m., (3) 90m., (4) 95m., (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting), , 7. The perimeter of the top of a, rectangul ar table is 2 8m.,, whereas its area is 48m2. What, is the length of its diagonal?, (1) 5m., (2) 10m., (3) 12m., (4) 12.5 m., (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , 8. If the length and the perimeter, of a rectangle are in the ratio, 5 : 16, then its length and, breadth will be in the ratio, (1) 5 : 11, (2) 5 : 8, (3) 5 : 4, (4) 5 : 3, (SSC CPO S.I. Exam. 09.11.2008), , 9. The length and perimeter of a, rectangle are in the ratio 5:18., Then length and breadth will be, in the ratio, (1) 4 : 3, (2) 3 : 5, (3) 5 : 4, (4) 4 : 7, (SSC Graduate Level Tier-I, Exam. 11.11.2012 (Ist Sitting), , 2. The perimeter of two squares are, 40 cm and 32 cm. The perimeter, of a third square whose area is, the difference of the area of the, two squares is, (1) 24 cm (2) 42 cm, (3) 40 cm (4) 20 cm, , 10. If the area of a rectangle be (x2 +, 7x + 10) sq. cm, then one of the, possible perimeter of it is, (1) (4x + 14) cm (2) (2x + 14) cm, (3) (x + 14) cm (4) (2x + 7) cm, , (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 3. If the ratio of areas of two, squares is 225 : 256, then the, ratio of their perimeter is :, (1) 225 : 256 (2) 256 : 225, (3) 15 : 16, (4) 16 : 15, , 11. The perimeter of a rectangular plot, is 48 m and area is 108 m2. The, dimensions of the plot are, (1) 36 m and 3 m, (2) 12 m and 9 m, (3) 27 m and 4 m, (4) 18 m and 6 m, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , (SSC Graduate Level Tier-I, Exam. 19.05.2013 Ist Sitting), , (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , SME–1132, , 12. The sides of a triangle are in the, ratio, , 1 1 1, : : . If the perimeter of, 2 3 4, , the triangle is 52 cm, the length, of the smallest side is :, (1) 24 cm, (2) 10 cm, (3) 12 cm, (4) 9 cm, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 13. The area of an equilateral triangle, is 400 3 sq.m. Its perimeter, is :, (1) 120 m (2) 150 m, (3) 90 m, (4) 135 m, (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 14. From a point in the interior of an, equi lat eral, triangl e,, the, perpendicular distance of the, sides are, , 3 cm, 2 3 cm and, , 5 3 cm. The perimeter (in cm) of, the triangle is, (1) 64, (2) 32, (3) 48, (4) 24, (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 15. The perimeter of a triangle is 30, cm and its area is 30 cm2. If the, largest side measures 13 cm, what, is the length of the smallest side, of the triangle ?, (1) 3 cm, (2) 4 cm, (3) 5 cm, (4) 6 cm, (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 16. The area of a triangle is 216 cm2, and its sides are in the ratio 3 :, 4 : 5. The perimeter of the triangle is :, (1) 6 cm, (2) 12 cm, (3) 36 cm, (4) 72 cm, (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 17. In a triangular field having sides, 30m, 72m and 78m, the length, of the altitude to the side measuring 72m is :, (1) 25 m, (2) 28 m, (3) 30 m, (4) 35 m, (SSC CPO S.I. Exam. 16.12.2007), , 18. If the perimeter of a right-angled, isosceles triangle is, , e4, , 2 +4, , j, , cm, the length of the hypotenuse, is :, (1) 4 cm, (2) 6 cm, (3) 8 cm, (4) 10 cm, (SSC CPO S.I. Exam. 16.12.2007)

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MENSURATION, 19. Through each vertex of a triangle, a line parallel to the opposite, side is drawn. The ratio of the, perimeter of the new triangle,, thus formed, with that of the, original triangle is, (1) 3 : 2, (2) 4 : 1, (3) 2 : 1, (4) 2 : 3, (SSC CPO S.I. Exam. 09.11.2008), , 20. The sides of a triangle are in the, , 1 1 1, : :, and its perimeter, 3 4 5, is 94cm. The length of the smallest side of the triangle is:, ratio, , (1) 18 cm, , (2) 22.5 cm, , (3) 24 cm, , (4) 27 cm, (SSC CHSL DEO & LDC, Exam. 27.11.2010), , 21. The length of two sides of an isosceles triangle are 15 and 22 respectively. What are the possible, values of perimeter ?, (1) 52 or 59, (2) 52 or 60, (3) 15 or 37, (4) 37 or 29, (SSC CISF Constable (GD), Exam. 05.06.2011), , 22. If the perimeter of a right-angled, triangle is 56 cm and area of the, triangle is 84 sq. cm, then the, length of the hypotenuse is (in cm), (1) 25, (2) 50, (3) 7, (4) 24, (SSC CHSL DEO & LDC Exam., 21.10.2012 (Ist Sitting), , 23. If the length of each median of, an equilateral triangle is 6 3 cm,, the perimeter of the triangle is, (1) 24 cm, (2) 32 cm, (3) 36 cm, (4) 42 cm, (SSC Graduate Level Tier-I, Exam. 11.11.2012 (Ist Sitting), , 24. The area of an equilateral triangle, is 4 3 sq. cm. Its perimeter is, (1) 12 cm, (2) 6 cm, (3) 8 cm, , (4) 3 3 cm, , (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , 25. The sides of a triangle are in the, , 1 1 1, : :, and its perimeter, 4 6 8, is 91 cm. The difference of the, length of longest side and that of, shortest side is, (1) 19 cm, (2) 20 cm, (3) 28 cm, (4) 21 cm, ratio, , (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , 26. The diagonals of a rhombus are, 32 cm and 24 cm respectively., The perimeter of the rhombus is:, (1) 80 cm, (2) 72 cm, (3) 68 cm, (4) 64 cm, (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 27. The diagonals of a rhombus are, 24 cm and 10 cm. The perimeter of the rhombus (in cm) is :, (1) 68, (2) 65, (3) 54, (4) 52, (SSC CGL Prelim Exam. 24.02.2002, (Second Sitting), , 28. The perimeter of a rhombus is, 40 cm. If one of the diagonals be, 12cm long, what is the length of, the other diagonal ?, (1) 12 cm, , (2), , 136 cm, , (3) 16 cm, , (4), , 44 cm, , (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone), , 29. The perimeter of a rhombus is 40, cm. If the length of one of its, diagonals be 12 cm, the length of, the other diagonal is, (1) 14 cm (2) 15 cm, (3) 16 cm (4) 12 cm, (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 30. The sides of a quadrilateral are, in the ratio 3 : 4 : 5 : 6 and its, perimeter is 72 cm. The length, of its greatest side (in cm) is, (1) 24, (2) 27, (3) 30, (4) 36, (SSC (South Zone) Investigator, Exam. 12.09.2010), , 31. The area of a rhombus is 216 cm2, and the length of its one diagonal, is 24 cm. The perimeter (in cm), of the rhombus is, (1) 52, (2) 60, (3) 120, (4) 100, (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 32. The area of a circle is 38.5 sq., cm. Its circumference (in cm) is, , FG use p = 22 IJ :, H, 7K, (1) 22, (3) 26, , 33. The diameter of a toy wheel is, 14 cm. What is the distance, travelled by it in 15 revolutions?, (1) 880 cm, (2) 660 cm, (3) 600 cm, (4) 560 cm, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 34. A can go round a circular path, 8 times in 40 minutes. If the, diameter of the circle is, increased to 10 times the, original diameter, the time, required by A to go round the, new path once travelling at the, same speed as before is :, (1) 25 min, (2) 20 min, (3) 50 min, (4) 100 min, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 35. Diameter of a wheel is 3 cm. The, wheel revolves 28 times in a, minute. To cover 5.280 km distance, the wheel will take (Take, , p=, , 22, ):, 7, , (1) 10 minutes (2) 20 minutes, (3) 30 minutes (4) 40 minutes, (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 36. Find the diameter of a wheel that, makes 113 revolutions to go 2 km, 26 decameters. (Take, (1) 4, , 4, m, 13, , (3) 12, , (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , SME–1133, , =, , 22, ), 7, , 4, m, 11, , 4, 8, m (4) 12, m, 11, 11, , (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 37. The radius of a circular wheel is, 1.75 m. The number of revolutions that it will make in travelling 11 km., is, (1) 1000, (2) 10,000, (3) 100, (4) 10, (SSC Section Officer (Commercial, Audit) Exam. 16.11.2003), (Second Sitting), , 38. A circular wire of radius 42 cm, is bent in the form of a rectangle, whose sides are in the ratio of, 6 : 5. The smaller side of the, rectangle is, , (2) 24, (4) 32, , (2) 6, , p, , (1) 60 cm, (3) 25 cm, , FG Take p = 22 IJ, H, 7 K, (2) 30 cm, (4) 36 cm, , (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting)

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MENSURATION, 39. The number of revolutions, a, wheel of diameter 40 cm makes, in travelling a distance of 176 m,, is, , FG Take p = 22 IJ, H, 7 K, , (1) 140, (3) 160, , (2) 150, (4) 166, , (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 40. If the difference between the circumference and diameter of a, circle is 30 cm, then the radius, of the circle must be, (1) 6 cm, (2) 7 cm, (3) 5 cm, (4) 8 cm, (SSC CPO S.I. Exam. 03.09.2006), , 41. If the perimeter of a semicircular, field is 144m, then the diameter, 22 I, F, J, of the field is GH take p =, 7K, , (1) 55m, (3) 28m, , (2) 30m, (4) 56m, , (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 42. The perimeter (in metres) of a, semicircle is numerically equal to, its area (in square metres). The, length of its d iameter is, , FG take p =, H, , 22, 7, , IJ, K, , 46. The diameter of a wheel is 98 cm., The number of revolutions in, which it will have to cover a, distance of 1540 m is, (1) 500, (2) 600, (3) 700, (4) 800, (SSC CGL Tier-1 Exam.19.06.2011, (First Sitting), , 47. The wheel of a motor car makes, 1000 revolutions in moving 440, m. The diameter (in metre) of the, wheel is, (1) 0.44, (2) 0.14, (3) 0.24, (4) 0.34, (SSC CGL Tier-1 Exam.19.06.2011, (Second Sitting), , 48. A bicycle wheel makes 5000 revolutions in moving 11km.Then the, radius of the wheel (in cm) is, (Take p =, , 22, 7, , ), , (1) 70, , (2) 35, , (3) 17.5, , (4) 140, , (SSC CGL Tier-1 Exam.26.06.2011, (First & Second Sitting), , 49. Three circles of diameter 10 cm, each, are bound together by a, rubber band, as shown in the figure., , 6, 6, (1) 3, metres (2) 5, metres, 11, 11, (3) 6, , 6, 2, metres (4) 6, metres, 11, 11, , (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 43. The ratio of the numbers giving, the measure of the circumference, and the area of a circle of radius, 3 cm is, (1) 1 : 3, (2) 2 : 3, (3) 2 : 9, (4) 3 : 2, (SSC CPO S.I. Exam. 09.11.2008), , 44. The ratio of the radii of two, wheels is 3 : 4. The ratio of their, circumference is, (1) 4 : 3, (2) 3 : 4, (3) 2 : 3, (4) 3 : 2, (SSC CGL Tier-I Exam. 16.05.2010, (Second Sitting), , 45. The length (in cm) of a chord of a, circle of radius 13 cm at a distance of 12 cm from its centre is, (1) 5, (2) 8, (3) 10, (4) 12, (SSC (South Zone) Investigator, Exam. 12.09.2010), , 51. A semicircular shaped window, has diameter of 63 cm. Its pe-, , FG, H, , rimeter equals p =, (1) 126 cm, (3) 198 cm, , 22, 7, , IJ, K, , (2) 162 cm, (4) 251 cm, , (SSC CISF Constable (GD), Exam. 05.06.2011), , 52. A gear 12 cm in diameter is turning a gear 18 cm in diameter., When the smaller gear has 42, revolutions, how many has the, larger one made ?, (1) 28, (2) 20, (3) 15, (4) 24, (SSC CHSL DEO & LDC Exam., 21.10.2012 (IInd Sitting), , 53. The perimeter of a semi-circular, area is 18cm, then the radius is :, (using p =, (1) 5, , 1, cm, 3, , (3) 6 cm, , 22, ), 7, (2) 3, , 1, cm, 2, , (4) 4 cm, , (SSC CHSL DEO & LDC Exam., 04.11.2012, Ist Sitting), , 54. A circular road runs around a, circular ground. If the difference, between the circumference of, the outer circle and the inner, circle is 66 metres, the width of, the road is:, (Take p =, , The length of the rubber band,, (in cm) if it is stretched as, shown, is, (1) 30, (2) 30 + 10p, (3) 10p, , (4) 60 + 20p, , (SSC CPO (SI, ASI & Intelligence Officer), Exam. 28.08.2011 (Paper-I), , 50. If a chord of length 16 cm is at, a distance of 15 cm from the centre of the circle, then the length, of the chord of the same circle, which is at a distance of 8 cm, from the centre is equal to, (1) 10 cm, (2) 20 cm, (3) 30 cm, (4) 40 cm, (SSC CPO (SI, ASI & Intelligence Officer), Exam. 28.08.2011 (Paper-I), , SME–1134, , 22, ), 7, , (1) 10.5 metres (2) 7 metres, (3) 5.25 metres (4) 21 metres, (SSC Graduate Level Tier-I, Exam. 21.04.2013, Ist Sitting), , 55. A person observed that he required 30 seconds less time to, cross a circular ground along its, diameter than to cover it once, along the boundary. If his speed, was 30 m/minute, then the radius of the circular ground is (Take, , p=, , 22, ) :, 7, , (1) 5.5 m, (3) 10.5 m, , (2) 7.5 m, (4) 3.5 m, , (SSC Graduate Level Tier-I, Exam. 21.04.2013)

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MENSURATION, 56. The difference of perimeter, and diameter of a circle is X unit., The diameter of the circle is, (1), , X, X, unit (2), unit, p -1, p +1, , (3), , X, unit, p, , (4), , FG X - 1IJ unit, Hp K, , (SSC Graduate Level Tier-I, Exam. 19.05.2013), , 57. The circumference of a circle is, 100 cm. The side of a square inscribed in the circle is, (1), , 62. A wire when bent in the form of, a square encloses an area of 484, sq. cm. What will be the enclosed, area when the same wire is bent, into the form of a circle?, (Take p =, , (1) 462 sq.cm (2) 539 sq.cm, (3) 616 sq.cm (4) 693 sq.cm, (SSC CGL Prelim Exam. 24.02.2002, (Ist Sitting) & (SSC CGL Prelim, Exam. 13.11.2005 (Ist Sitting), & (SSC CHSL DEO & LDC, Exam. 11.12.2011 (Ist Sitting,, Delhi Zone), , 100 2, 50 2, cm (2), cm, p, p, , 100, (3), cm, p, , (4) 50, , 2 cm, , (SSC CPO S.I. Exam. 12.01.2003, & 09.11.2008), , 58. A path of uniform width surrounds a circular park. The difference of internal and external, circumference of this circular, path is 132 metres. Its width is :, (Take p =, (1) 22m, (3) 21m, , 22, ), 7, , 63. Four equal sized maximum circular, plates are cut off from a square, paper sheet of area 784 sq.cm., The circumference of each plate, , (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 59. The ratio of the outer and the inner perimeter of a circular path, i s 23 : 22. If the path i s 5, metres wide, the diameter of the, inner circle is :, (1) 110 m, (2) 55 m, (3) 220 m, (4) 230 m, (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 60. The radius of the incircle of a triangle is 2 cm. If the area of the, triangle is 6 cm2, then its perimeter is, (1) 2 cm, (2) 3 cm, (3) 6 cm, (4) 9 cm, (SSC CPO (SI, ASI & Intelligence Officer), Exam.28.08.2011 (Paper-I), , 61. The area of the circumcircle of, an equilateral triangle is 3p sq., cm. The perimeter of the triangle is, (2) 9 cm, (4) 3 cm, , (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , LM Take p = 22 OP, 7 Q, N, (1) 125 cm2, (3) 550 cm2, , (2) 230 cm2, (4) 616 cm2, , (SSC Graduate Level Tier-II, Exam.16.09.2012), , 68. If the sides of an equilateral triangle are increased by 20%, 30%, and 50% respectively to form a, new triangle, the increase in the, perimeter of the equilateral triangle is, , 1, %, 3, , (1) 25%, , (2) 33, , (3) 75%, , (4) 100%, , (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting), , is (Take p =, , 22, ), 7, , (1) 22 cm, , (2) 44 cm, , (3) 66 cm, , (4) 88 cm, , (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , (2) 20 m, (4) 24m, , (1) 3 3 cm, (3) 18 cm, , 22, ), 7, , 67. A circle and a rectangle have the, same perimeter. The sides of the, rectangle are 18 cm and 26 cm., The area of the circle is, , 64. If the area of a circle and a square, are equal, then the ratio of their, perimeter is, (1) 1 : 1, , (2), , (3) p : 2, , (4), , 2: p, , (SSC CGL Prelim Exam. 13.11.2005, (Second Sitting), , 65. A copper wire is bent in the form, of square with an area of 121, cm2. If the same wire is bent in, the form of a circle, the radius (in, , (1) 7, , (2) 10, , (3) 11, , (4) 14, , FG Take p = 22 IJ, H, 7 K, (1) 70 m, (3) 80 m, , p:2, , cm) of the circle is (Take p =, , 69. A horse is tied to a post by a rope., If the horse moves along a circular path always keeping the rope, stretched and describes 88 metres when it has traced out 72°, at the centre, the length of the, rope is, , 22, ), 7, , (SSC CGL Tier-1 Exam.19.06.2011, , (2) 75 m, (4) 65 m, , (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 70. Three circles of radii 3.5 cm, 4.5, cm and 5.5 cm touch each other, externally. Then the perimeter of, the triangle formed by joining the, centres of the circles, in cm, is, (1) 27, (2) p[(3.5)2 + (4.5)2 + (5.5)2], (3) 27p, (4) 13.5, (SSC CGL Tier-I Re-Exam. (2013), 20.07.2014 (IInd Sitting), , (SSC Assistant Grade-III, , 71. ABCD is a parallelogram in which, diagonals AC and BD intersect, at O. If E, F, G and H are the, mid points of AO, DO, CO and, BO respectively, then the ratio, of the perimeter of the quadrilateral EFGH to the perimeter of, parallelogram ABCD is, (1) 1 : 4, (2) 2 : 3, (3) 1 : 2, (4) 1 : 3, , Exam. 11.11.2012 (IInd Sitting), , (SSC CGL Tier-I Exam. 19.10.2014), , (Second Sitting), , 66. If the perimeter of a square and, a rectangle are the same, then, the area P and Q enclosed by them, would satisfy the condition, (1) P < Q, (3) P > Q, , (2) P < Q, (4) P = Q, , SME–1135

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MENSURATION, 72. A circular wire of diameter 112, cm is cut and bent in the form of, a rectangle whose sides are in the, ratio of 9 : 7. The smaller side of, the rectangle is, (1) 77 cm, , (2) 97 cm, , (3) 67 cm, , (4) 87 cm, , (SSC CGL Tier-I Exam. 26.10.2014), , 73. If the perimeter of an equilateral, triangle be 18 cm, then the length, of each median is, (1) 3 2 cm, , (2) 2 3 cm, , (3) 3 3 cm, , (4) 2 2 cm, , (SSC CHSL DEO & LDC Exam., 02.11.2014 (IInd Sitting), , 74. Two equal maximum sized circular plates are cut off from a circular paper sheet of circumference 352 cm. Then the circumference of each circular plate is, (1) 176 cm, (2) 150 cm, (3) 165 cm, (4) 180 cm, (SSC CHSL DEO & LDC, Exam. 16.11.2014), , 75. If diagonals of a rhombus are 24, cm and 32 cm, then perimeter of, that rhombus is, (1) 80 cm, (2) 84 cm, (3) 76 cm, (4) 72 cm, (SSC CHSL DEO & LDC, Exam. 16.11.2014), , 76. The inradius of an equilateral triangle is 3 cm, then the perimeter of that triangle is, (1) 18 cm, (2) 15 cm, (3) 12 cm, (4) 6 cm, (SSC CHSL DEO & LDC, Exam. 16.11.2014), , 77. Length of a side of a square inscribed in a circle is a 2 units., The circumference of the circle is, (1) 2 pa units (2) pa units, (3) 4 pa units, , (4), , 2a, units, p, , (SSC CHSL DEO Exam. 02.11.2014, (Ist Sitting), , 78. The perimeter and length of a, rectangle are 40 m and 12 m respectively. Its breadth will be, (1) 10 m, (2) 8 m, (3) 6 m, (4) 3 m, (SSC CHSL DEO Exam. 02.11.2014, (Ist Sitting), , 79. The difference between the circumference and diameter of a, circle is 150 m. The radius of that, , 22, ), 7, , circle is (Take p =, (1) 25 metre, (3) 30 metre, , (2) 35 metre, (4) 40 metre, , (SSC CHSL DEO Exam. 16.11.2014, , 85. Quadrilateral, ABCD, is, circumscribed about a circle. If, the lengths of AB, BC and CD are, 7 cm, 8.5 cm, and 9.2 cm, respectively, then the length (in, cm) of DA is, (1) 7.7, (2) 16.2, (3) 10.7, (4) 7.2, , (Ist Sitting), , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 80. PQRS is a square with side 10, cm. A, B, C and D are mid–points, of PQ, QR, RS and SP respectively. Then the perimeter of the, square ABCD so formed is, , 86. The perimeter of a rhombus is 60, cm and one of its diagonal is 24, cm. The area of the rhombus is, (1) 108 sq. cm. (2) 216 sq. cm., (3) 432 sq. cm. (4) 206 sq. cm., , (1) 10 2 cm, , (2) 20 2 cm, , (3) 25 2 cm, , (4) 15 2 cm, , (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014 , Ist Sitting, TF No. 333 LO 2), , 81. A piece of wire when bent to form, a circle will have a radius of 84, cm. If the wire is bent to form a, square, the length of a side of the, square is, (1) 152 cm, (2) 132 cm, (3) 168 cm, , (4) 225 cm, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 82. The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first, triangle is 9 cm. Determine the, corresponding side of the second, triangle., (1) 13.5 cm, (2) 6 cm, (3) 15 cm, (4) 5 cm, (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 83. The sides of a triangle having, area 7776 sq. cm are in the ratio 3 : 4 : 5. The perimeter of, the triangle is, (1) 432 cm, (3) 412 cm, , (2) 400 cm, (4) 424 cm, , (SSC CGL Tier-I Exam, 09.08.2015, (Ist Sitting) TF No. 1443088), , 84. The diameter of each wheel of a, car is 70 cm. If each wheel rotates 400 times per minute, then, the speed of the car (in km/hr), is, , FG Take p = 22 IJ, H, 7 K, , (1) 0.528, , (2) 528, , (3) 52.8, , (4) 5.28, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , SME–1136, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 87. The ratio of circumference and, diameter of a circle is 22 : 7. If, the circumference be 1, , 4, m,, 7, , then the radius of the circle is :, (1), , 1, m, 3, , (2), , 1, m, 2, , (3), , 1, m, 4, , (4) 1 m, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (Ist Sitting) TF No. 6636838), , 88. Four circles of equal radii are, described about the four corners, of a square so that each touches, two of the other circles. If each, side of the square is 140 cm then, area of the space enclosed between the circumference of the, , FG, H, , circle is Take p =, (1) 4200 cm2, (3) 7000 cm2, , 22, 7, , IJ, K, , (2) 2100 cm2, (4) 2800 cm2, , (SSC CGL Tier-II Online, Exam.01.12.2016), , 89. The perimeter of a triangle is 67, cm. The first side is twice the, length of the second side. The, third side is 11 cm more than the, second side. Find the length of, the shortest side of the triangle., (1) 12 cm., (2) 14 cm., (3) 17 cm., (4) 25 cm., (SSC CPO SI, ASI Online, Exam.05.06.2016) (IInd Sitting), , 90. The radius of a wheel is 25 cm., How many rounds it will take to, complete 11 km., (1) 5000, (2) 6000, (3) 7000, (4) 4000, (SSC CPO SI, ASI Online, Exam.05.06.2016) (IInd Sitting), , 91. If the perimeter of circle A is equal

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MENSURATION, to perimeter of semi circle B,, what is the ratio of their areas ?, , b g, , (1) p + 2, , 2, , (4), , (2) 48, (4) 26, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , : 2p2, , 96. In an isosceles triangle, the, length of each equal side is twice, the length of the third side. The, ratio of areas of the isosceles triangle and an equilateral triangle, with same perimeter is, , b g, bp + 2g : 4p, 4p : bp + 2g, , (2) 2p2 : p + 2, (3), , (1) 52, (3) 32, , 2, , 2, , 2, 2, , 2, , (SSC CPO Exam. 06.06.2016), (Ist Sitting), , 92. PS is a diameter of a circle of radius 6 cm. In the diameter PS, Q, and R are two points such that, PQ, QR and RS are all equal., Semicircles are drawn on PQ and, QS as diameter (as shown in the, figure). The perimeter of shaded, portion is :, , (1) 30 5 : 100 (2) 32 5 : 100, , Q, , 6, (1) 15, cm, 7, (3) 37, , 5, cm, 7, , R, , S, , 3, (2) 75, cm, 7, (4) 18, , 6, cm, 7, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , 93. The perimeter of a certain isosceles right triangle is 10 + 10 2, cm. What is the length of the, hypotenuse of the triangle ?, (1) 5 cm, (2) 10 cm, (3) 5 2 cm, , (4) 10 2 cm, , (SSC CPO SI & ASI, Online, Exam. 06.06.2016) (IInd Sitting), , 94. The radius of wheel moving on a, , 3, road, is 8, 4, , cm. How many, , rounds it will take to complete 55, metre distance., (1) 10, (2) 11, (3) 100, (4) 55, (SSC CPO SI & ASI, Online, Exam. 06.06.2016) (IInd Sitting), , 95. The sides of a triangle are in the, ratio, , 1 1 1, :, :, and its perim2 3, 4, , eter is 104 cm. The length of the, longest side (in cm) is, , walks 2, , 9, m a minute, the time, 20, , taken by him to walk one round, around it is approximately., (1) 50.82 minutes, (2) 54.82 minutes, (3) 54.62 minutes, (4) 50.62 minutes, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , (3) 36 5 : 100 (4) 42 5 : 100, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 97. The radius of the incircle of an, equilateral D ABC of side 2 3, units is x cm. The value of x is :, (1), , 1, 3, , (2), , (3) 1, , P, , 103. A square playground measures, 1127.6164 sq. cm. If a man, , 1, 2, , (4), , 3, , TYPE–III, 1. How many tiles, each 4 decimetre, square, will be required to cover, the floor of a room 8 m long and 6, m broad ?, (1) 200, (2) 260, (3) 280, (4) 300, , (SSC CGL Tier-I (CBE), Exam. 28.08.2016 (Ist Sitting), , (SSC Graduate Level Tier-II, , 98. The four sides of a quadrilateral, are in the ratio of 2 : 3 : 4 : 5 and, its perimeter is 280 metre. The, length of the longest side is :, (1) 100 metre (2) 150 metre, (3) 175 metre (4) 180 metre, , 2. The floor of a corridor is 100m, long and 3 m wide. Cost of covering the floor with carpet 50 cm, wide at the rate of 15 per m is, (1) 4500, (2) 9000, (3) 7500, (4) 1900, , (SSC CGL Tier-I (CBE), Exam. 07.09.2016 (IInd Sitting, , 99. If x is the area, y is the circumference and z is the diameter of, , x, , circle then the value of yz is, (1) 4 : 1, (3) 1 : 2, , (2) 1 : 4, (4) 2 : 1, , (SSC CGL Tier-I (CBE), Exam. 08.09.2016 (IInd Sitting), , 100. The lengths of diagonals of a, rhombus are 24 cm and 10 cm, the perimeter of the rhombus (in, cm.) is :, (1) 52, (2) 56, (3) 68, (4) 72, , Exam. 29.09.2013, , (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting), , 3. Three sides of a triangular field, are of length 15 m, 20 m and 25, m long respectively. Find the cost, of sowing seeds in the field at the, rate of 5 rupees per sq.m., (1) 300, (2) 600, (3) 750, (4) 150, (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 4. The radius of a circular wheel is, 1.75 m. The number of revolutions it will make in travelling 11, km is :, , FG use p = 22 IJ, H, 7 K, , (SSC CGL Tier-I (CBE), Exam. 08.09.2016 (IIIrd Sitting), , 101. The length of the base of an isosceles triangle is 2x – 2y + 4z,, and its perimeter is 4x – 2y +, 6z. Then the length of each of, the equal sides is, (1) x + y, (2) x + y + z, (3) 2 (x + y), (4) x + z, (SSC CGL Tier-I (CBE), Exam. 09.09.2016 (IInd Sitting), , 102. Which of the following ratios can, be the ratio of the sides of a right, angled triangle?, (1) 9 : 6 : 3, (2) 13 : 12 : 5, (3) 7 : 6 : 5, (4) 5 : 3 : 2, (SSC CGL Tier-I (CBE), Exam. 11.09.2016 (IIIrd Sitting), , SME–1137, , (1) 800, (3) 1000, , (2) 900, (4) 1200, , (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 5. The radius of a wheel is 21 cm., How many revolutions will it, make in travelling 924 metres ?, , FG use p = 22 IJ, H, 7 K, (1) 7, (3) 200, , (2) 11, (4) 700, , (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting)

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MENSURATION, 6. A playground is in the shape of, a rectangle. A sum of 1,000, was spent to make the ground, usable at the rate of 25 paise per, sq. m. The breadth of the ground, is 50 m. If the length of the, ground is increased by 20 m,, what will be the expenditure (in, rupees) at the same rate per sq., m. ?, (1) 1,250, (2) 1,000, (3) 1,500, (4) 2,250, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 7. If each edge of a square be doubled, then the increase percentage in its area is, (1) 200%, (2) 250%, (3) 280%, (4) 300%, (SSC CHSL DEO & LDC, Exam. 16.11.2014), , 8. If radius of a circle is increased, by 5%, then the increase in its, area is, (1) 10.25 %, (2) 10 %, (3) 5.75 %, , (4) 5 %, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 9. The height of a triangle is increased by 10%. To retain the, original area of the triangle, its, corresponding base must be decreased by, (1) 10%, (3) 9, , 1, %, 8, , (2) 9, , 1, %, 7, , (4) 9, , 1, %, 11, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 10. The percentage increase in the, area of a rectangle, if each of its, sides is increased by 20% is, equal to, (1) 32%, (3) 42%, , (2) 34%, (4) 44%, (SSC CGL Tier-I, Re-Exam, 30.08.2015), , 11. If the radius of a circle is decreased by 10%, then the area, of the circle is decreased by, (1) 89%, (2) 18%, (3) 19%, (4) 25%, (SSC Constable (GD), , 12. The outer circumference of a circular race-track is 528 metre. The, track is everywhere 14 metre, wide. Cost of levelling the track, at the rate of Rs. 10 per sq. metre is :, (1) Rs. 77660 (2) Rs. 66760, (3) Rs. 76760 (4) Rs. 67760, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (IInd Sitting) TF No. 3441135), , 13. If the area of a square is increased by 44%, retaining its, shape as a square, each of its, sides increases by :, (1) 19%, (2) 21%, (3) 22%, (4) 20%, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , 14. What will be the percentage increase in the area of a square, when each of the its sides is increased by 10%?, (1) 20, (2) 11, (3) 121, (4) 21, (SSC CGL Tier-I (CBE), Exam. 30.08.2016) (IInd Sitting), , 15. If the length and breadth of a, rectangle are increased by 10%, and 8% respectively, then the, area of the rectangle increases, by :, (1) 18, , 7, %, 5, , (3) 18%, , (2) 18, (4) 18, , 4, %, 5, 1, %, 5, , (SSC CGL Tier-I (CBE), Exam. 27.10.2016 (Ist Sitting), , TYPE–IV, 1. The edges of a rectangular box, are in the ratio 1 : 2 : 3 and its, surface area is 88 cm2. The volume of the box is, (1) 24 cm3, (2) 48 cm3, 3, (3) 64 cm, (4) 120 cm3, (SSC CHSL DEO & LDC Exam., 28.10.2012, Ist Sitting), , 2. A right triangle with sides 3 cm,, 4 cm and 5 cm is rotated about, the side 3 cm to form a cone, The, volume of the cone so formed is, (1) 16 p cm3, (2) 12 p cm3, 3, (3) 15 p cm, (4) 20 p cm3, (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , Exam, 04.10.2015, IInd Sitting), , SME–1138, , 3. If the length of each side of a regular tetrahedron is 12 cm, then, the volume of the tetrahedron is, (1) 144 2 cu. cm., (2) 72, , 2 cu. cm., , (3) 8 2 cu. cm., (4) 12 2 cu. cm., (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (Delhi Zone), , 4. Two right circular cylinders of, equal volume have their heights, in the ratio 1 : 2. The ratio of, their radii is :, (1), , 2 :1, , (3) 1 : 2, , (2) 2 : 1, (4) 1 : 4, , (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 5. The volume of a right circular cylinder whose height is 40cm, and, circumference of its base is 66, cm, is :, (1) 55440 cm3 (2) 3465 cm3, (3) 7720 cm3 (4) 13860 cm3, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , 6. The base radii of two cylinders, are in the ratio 2 : 3 and their, heights are in the ratio 5 : 3. The, ratio of their volumes is :, (1) 27 : 20, (2) 20 : 27, (3) 9 : 4, (4) 4 : 9, (SSC CGL Prelim Exam. 24.02.2002, & 13.11.2005 (Ist Sitting), , 7. The curved surface area of a, cylindrical pillar is 264 m2 and, its volume is 924 m3., , FG Taking p = 22IJ . Find the ratio, H, 7K, , of its diameter to its height., (1) 7 : 6, (2) 6 : 7, (3) 3 : 7, (4) 7 : 3, (SSC CGL Prelim Exam. 24.02.2002, (IInd Sitting) & (SSC CGL Prelim, Exam. 13.11.2005 (Ist Sitting), & CHSL DEO & LDC, Exam. 11.12.2011 (IInd Sitting,, East Zone), , 8. A hollow cylindrical tube 20 cm, long, is made of iron and its, external and internal diameters, are 8 cm and 6 cm respectively., The volume of iron used in making, the tube is (p =, , 22, ), 7, , (1) 1760 cu.cm. (2) 880 cu.cm., (3) 440 cu.cm. (4) 220 cu.cm., (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting)

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MENSURATION, 9. A hollow iron pipe is 21 cm long, and its exterior diameter is 8 cm., If the thickness of the pipe is 1, cm and iron weighs 8 g/cm3,, then the weight of the pipe is, , FG Take p = 22 IJ, H, 7 K, (1) 3.696 kg, (3) 36 kg, , (2) 3.6 kg, (4) 36.9 kg, , (SSC CGL Prelim Exam. 08.02.2004, (IInd Sitting) & (SSC CHSL DEO, & LDC Exam. 04.12.2011), , 10. The volume of a right circular, cylinder, 14 cm in height, is equal, to that of a cube whose edge is, , 22, the radius, 7, of the base of the cylinder is, (1) 5.2 cm., (2) 5.5 cm., (3) 11.0 cm. (4) 22.0 cm., , 11 cm. Taking p =, , (SSC CPO S.I. Exam. 05.09.2004), , 11. If the volume of a right circular, cylinder is 9ph m3, where h is, its height (in metres) then the diameter of the base of the cylinder is equal to, (1) 3 m, (2) 6 m, (3) 9 m, (4) 12 m, (SSC CPO S.I. Exam. 05.09.2004), , 12. A right circular cylinder of height, 16 cm is covered by a rectangular tin foil of size 16 cm × 22 cm., The volume of the cylinder is, (1) 352 cm3, (2) 308 cm3, (3) 616 cm3, (4) 176 cm3, (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 13. The volume of the metal of a cylindrical pipe is 748 cm3. The, length of the pipe is 14cm and, its external radius is 9 cm. Its, thickness is, (1) 1 cm, (3) 2.3 cm, , FG Take p = 22 IJ, H, 7K, (2) 5.2 cm, (4) 3.7 cm, , (SSC CGL Prelim Ex am. 27.07.2008, (First Sitting), , 14. Two iron sheets each of diameter 6 cm are immersed in the, water contained in a cylindrical, vessel of radius 6 cm. The level, of the water in the vessel will be, raised by, (1) 1 cm, (2) 2 cm, (3) 3 cm, (4) 6 cm, (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , 15. The radii of the base of two, cylinders A and B are in the ratio, 3 : 2 and their height in the ratio, n : 1. If the volume of cylinder A, is 3 times that of cylinder B, the, value of n is, , 21. From a solid cylinder whose, height is 12 cm and diameter, 10cm, a conical cavity of same, height and same diameter of the, base is hollowed out. The volume, of the remaining solid is approx-, , FG, H, , IJ, K, , (1), , 4, 3, , (2), , 2, 3, , imately p =, , (3), , 3, 4, , (4), , 3, 2, , (1) 942.86 cm3 (2) 314.29 cm3, (3) 628.57 cm3 (4) 450.76 cm3, , (SSC CPO S.I. Exam. 09.11.2008), , 16. Water is being pumped out, through a circular pipe whose, internal diameter is 7cm. If the, flow of water is 12 cm per second, how many litres of water is, being pumped out in one hour ?, (1) 1663.2, (2) 1500, (3) 1747.6, (4) 2000, (SSC CPO S.I. Exam. 06.09.2009), , 17. The lateral surface area of a cylinder is 1056 cm2 and its height, is 16cm. Find its volume., (1) 4545 cm3 (2) 4455 cm3, (3) 5445 cm3 (4) 5544 cm3, (SSC CPO S.I. Exam. 06.09.2009), , 18. A cylinder has 'r' as the radius of, the base and 'h' as the height., The radius of base of another, cylinder, having double the volume but the same height as that, of the first cylinder must be, equal to, (1), , r, 2, , (3) r 2, , (SSC Constable (GD) & Rifleman, (GD) Exam. 22.04.2012 (IInd Sitting), , 22. The radius of a cylinder is 10, cm and height is 4 cm. The number of centimetres that may be, added either to the radius or to, the height to get the same increase in the volume of the cylinder is, (1) 5 cm, (2) 4 cm, (3) 25 cm, (4) 16 cm, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 23. The radii of the base of a cylinder and a cone are in the, ratio 3 : 2 and their heights, are in the ratio 2 : 3 . Their, volumes are in the ratio of, (1), , 3: 2, , (2) 3 3 : 2, , (3), , 3:2 2, , (4) 2 : 6, , (SSC Graduate Level Tier-I, Exam. 11.11.2012 (Ist Sitting), , (2) 2r, (4), , 2r, , FCI Assistant Grade-III, Exam. 25.02.2012 (Paper-I), North Zone (Ist Sitting), , 19. The diameter of two cylinders,, whose volumes are equal, are in, the ratio 3 : 2. Their heights will, be in the ratio ., (1) 4 : 9, (2) 5 : 6, (3) 5 : 8, (4) 8 : 9, (SSC CHSL DEO & LDC Exam., 28.11.2010 (Ist Sitting), , 20. From a solid cylinder of height, 10 cm and radius of the base 6, cm, a cone of same height and, same base is removed. The volume of the remaining solid is :, (1) 240 p cu.cm (2) 5280 cu.cm, (3) 620 p cu.cm (4) 360 p cu.cm, (SSC CHSL DEO & LDC, Exam. 11.12.2011 (IInd Sitting, (East Zone), , SME–1139, , 22, 7, , 24. The curved surface area and the, total surface area of a cylinder, are in the ratio 1 : 2. If the total, surface area of the right cylinder, is 616 cm2, then its volume is :, (1) 1232 cm3, (2) 1848 cm3, (3) 1632 cm3, (4) 1078 cm3, (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 25. The perimeter of the base of a, right circular cylinder is ‘a’ unit., If the volume of the cylinder is V, cubic unit, then the height of the, cylinder is, (1), , 4a 2 V, 4 pa 2, unit (2), unit, p, V, , (3), , 4 pV, pa 2 V, unit (4), unit, a2, 4, (SSC Graduate Level Tier-I, Exam. 19.05.2013)

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MENSURATION, 26. What is the height of a cylinder, that has the same volume and, radius as a sphere of diameter, 12 cm ?, (1) 7 cm, , (2) 10 cm, , (3) 9 cm, , (4) 8 cm, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 27. If diagonal of a cube is, , 12 cm,, then its volume in cubic cm is :, (1) 8, (2) 12, (4) 3 2, , (3) 24, , (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 28. If the volume of two cubes are, in the ratio 27:1, the ratio of, their edge is :, (1) 3 : 1, (2) 27:1, (3) 1:3, (4) 1:27, (SSC CGL Prelim Exam. 04.07.1999, (IInd Sitting) & (SSC S.O. Commercial, Audit Exam. 16.11.2003), , 29. The edges of a cuboid are in the, ratio 1 : 2 : 3 and its surface, area is 88cm 2. The volume of, the cuboid is :, (1) 120 cm3 (2) 64 cm3, (3) 48 cm, , 3, , (4) 24 cm, , 3, , (SSC CGL Prelim Exam. 04.07.1999 (IInd, Sitting) & (SSC CHSL DEO, & LDC Exam. 28.10.2012), , 30. What is the volume of a cube (in, cubi c cm) whose d iagonal, measures 4 3 cm?, (1) 16, (3) 64, , (2) 27, (4) 8, , (SSC CGL Prelim Exam. 24.02.2002, (Ist Sitting) & (SSC CPO S.I., Exam. 03.09.2006), , 31. A cuboidal water tank has 216, , 1, litres of water. Its depth is, of, 3, its length and breadth is, , 1, of, 2, , 32. A wooden box measures 20 cm by, 12 cm by 10 cm. Thickness of, wood is 1 cm. Volume of wood to, make the box (in cubic cm) is, (1) 960, (2) 519, (3) 2400, (4) 1120, (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 33. The area of three adjacent faces, of a cuboid are x, y, z square, units respectively. If the volume, of the cuboid be y cubic units,, then the correct relation between, v, x, y, z is, (1) v2 = xyz, (2) v3 = xyz, 2, 3, 3, 3, (3) v = x y z (4) v3 = x2y2z2, , (1) 900, (3) 1800, , 34. Water flows into a tank which is, 200m long and 150m wide,, through a pipe of cross-section, 0.3m × 0.2m at 20 km/hour., Then the time (in hours) for the, water level in the tank to reach, 8m is, (1) 50, (2) 120, (3) 150, (4) 200, (SSC CGL Tier-1 Exam. 19.06.2011, (First Sitting), , 35. A rectangular sheet of metal is, 40cm by 15cm. Equal squares of, side 4cm are cut off at the corners, and the remainder is folded up to, form an open rectangular box., The volume of the box is, (1) 896 cm3, (2) 986 cm3, (3) 600 cm3, (4) 916 cm3, (SSC CGL Tier-1 Exam. 19.06.2011, (First Sitting), , 36. The areas of three consecutive, faces of a cuboid are 12 cm2, 20, cm2 and 15 cm2, then the volume, (in cm3) of the cuboid is, (1) 3600, (2) 100, (3) 80, (4) 60, (SSC CGL Tier-1 Exam. 19.06.2011, (Second Sitting), , 37. Surface areas of three adjacent, faces of a cuboid are p, q, r. Its, volume is, pq 2 + qr 2 + rp 2, , (1), (2), , breadth. The length of the tank is, (1) 72 dm (2) 18 dm, (3) 6 dm, (4) 2 dm, , (3), (4), , e, , pq + qr + rp, , jep 2 + q 2 + r 2 j, , FG e p 2 + q 2 + r 2 j(p + q + r ) IJ, H, K, pqr, (SSC CHSL DEO & LDC Exam., 28.11.2010 (IInd Sitting), , SME–1140, , (2) 1200, (4) 720, (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 39. If the total surface area of a cube, is 96 cm2, its volume is, (1) 56 cm3, (3) 64 cm3, , (2) 16 cm3, (4) 36 cm3, (SSC CHSL DEO & LDC, , (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting), , 1, of the difference of length and, 3, , (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone) & (SSC CGL Prelim, Exam. 13.11.2005 (First Sitting), , 38. A godown is 15 m long and 12 m, broad. The sum of the area of the, floor and the ceiling is equal to, the sum of areas of the four walls., The volume (in m 3) o f the, godown is:, , Exam. 20.10.2013), , 40. The ratio of the volume of two, cones is 2 : 3 and the ratio of radii, of their base is 1 : 2. The ratio of, their height is, (1) 3 : 8, (3) 4 : 3, , (2) 8 : 3, (4) 3 : 4, , (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone) & (SSC CPO S.I. Exam., 03.09.2006) & (SSC CHSL DEO, & LDC Exam. 10.11.2013), , 41. If the height of a given cone be, doubled and radius of the base, remains the same, the ratio of, the volume of the given cone to, that of the second cone will be, (1) 2 : 1, (2) 1 : 8, (3) 1 : 2, , (4) 8 : 1, , (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 42. If the radius of the base of a, cone be doubled and height is, left unchanged, then ratio of the, volume of new cone to that of the, original cone will be :, (1) 1 : 4, (2) 2 : 1, (3) 1 : 2, , (4) 4 : 1, , (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 43. Each of the measure of the radius of base of a cone and that, of a sphere is 8 cm. Also, the, volume of these two solids are, equal. The slant height of the, cone is, (1) 8 17 cm, , (2) 4 17 cm, , (3) 34 2 cm, , (4) 34 cm., , (SSC CPO S.I. Exam. 05.09.2004)

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MENSURATION, 44. A cone of height 15 cm and, basediameter 30 cm is carved out, of a wooden sphere of radius 15, cm. The percentage of wasted, wood is :, (1) 75%, (2) 50%, (3) 40%, (4) 25%, , 50. Two solid right cones of equal, height and of radii r1 and r2 are, melted and made to form a solid, sphere of radius R. Then the, height of the cone is, , r12, , (3), , r12, , (SSC CPO S.I. Exam. 26.05.2005), , 45. In a right circular cone, the radius of its base is 7 cm and its, height 24 cm. A cross-section is, made through the midpoint of the, height parallel to the base. The, volume of the upper portion is, (1) 169 cm3, (2) 154 cm3, 3, (3) 1078 cm, (4) 800 cm3, (SSC Section Officer (Commercial, Audit) Exam.26.11.2006, (Second Sitting), , 46. If the area of the base of a cone is, 770 cm 2 and the area of the, curved surface is 814 cm2, then, its volume (in cm3) is :, (1) 213 5, , (2) 392 5, , (3) 550 5, , (4) 616 5, , (SSC CPO S.I. Exam. 16.12.2007), , 47. Volume of two cones are in the, ratio 1 : 4 and their diameters are, in the ratio 4 : 5. The ratio of their, height is, (1) 1 : 5, (2) 5 : 4, (3) 5 : 16, (4) 25 : 64, (SSC CPO S.I. Exam. 06.09.2009), , 48. The height of the cone is 30 cm., A small cone is cut off at the top, by a plane parallel to its base. If, , 1, of the volume, 27, of the cone, at what height, above, the base, is the section made?, (1) 6 cm, (2) 8 cm, (3) 10 cm, (4) 20 cm, , its volume is, , (SSC Data Entry Operator, Exam. 31.08.2008), , 49. The radius of the base and height, of a right circular cone are in the, ratio 5 : 12. If the volume of the, , 2, cm 3, the slant, 7, height (in cm) of the cone will be, (1) 12, (2) 13, (3) 15, (4) 17, cone is 314, , (SSC Data Entry Operator, Exam. 02.08.2009), , 4R 2, , (1), , + r22, , 4R 3, + r22, , 4R, , (2) r + r, 1, 2, (4), , (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , R2, r12, , + r22, , (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (North Zone), , 51. The ratio of radii of two cone is, 3 : 4 and the ratio of their height, is 4 : 3. Then the ratio of their, volume will be, (1) 3 : 4, (2) 4 : 3, (3) 9 : 16, (4) 16 : 9, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (North Zone), , 52. If a right circular cone is separated into solids of volumes V1, V2 ,, V3 by two planes parallel to the, base, which also trisect the altitude, then V1 : V2 : V3 is, (1) 1: 2 : 3, (2) 1: 4 : 6, (3) 1: 6 : 9, (4) 1: 7 : 19, (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (East Zone), , 53. If the radii of the circular ends of, a truncated conical bucket which, is 45cm high be 28 cm and 7 cm,, then the capacity of the bucket in, , FG, H, , 22, cubic centimetre is use p =, 7, (1) 48510, (2) 45810, (3) 48150, , IJ, K, , (4) 48051, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (Delhi Zone), , 54. The ratio of height and the diameter of a right circular cone is 3 :, 2 and its volume is 1078 cc, then, (taking p =, , 22, ) its height is :, 7, , (1) 7 cm, (3) 21 cm, , (2) 14 cm, (4) 28 cm, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (Delhi Zone), , 55. The radius of the base of a right, circular cone is doubled keeping, its height fixed. The volume of the, cone will be :, (1) three times of the previous volume, (2) four times of the previous volume, (3), , 2 times of the previous volume, (4) double of the previous volume, (SSC CHSL DEO & LDC Exam., 21.10.2012 (IInd Sitting), , SME–1141, , 56. The heights of two cones are in, the ratio 1 : 3 and the diameters, of their base are in the ratio 3 : 5., The ratio of their volume is, (1) 3 : 25, (2) 4 : 25, (3) 6 : 25, (4) 7 : 25, , 57. The base of a right circular cone, has the same radius a as that of, a sphere. Both the sphere and the, cone have the same volume., Height of the cone is, (1) 3a, (2) 4a, (3), , 7, a, 4, , (4), , 7, a, 3, , (SSC CHSL DEO & LDC Exam., 28.10.2012, Ist Sitting), , 58. The circumference of the base of, a 16cm height solid cone is 33cm., What is the volume of the cone in, cm3 ?, (1) 1028, (2) 616, (3) 462, (4) 828, (SSC CHSL DEO & LDC Exam., 04.11.2012, Ist Sitting), , 59. The perimeter of the base of a right, circular cone is 8 cm. If the height, of the cone is 21 cm, then its volume is:, (1) 108 p cm3, , (2), , 112, cm3, p, , (3) 112 p cm3, , (4), , 108, cm3, p, , (SSC Graduate Level Tier-I, Exam. 21.04.2013, Ist Sitting), , 60. If the volume of two right circular, cones are in the rati o, 4 : 1 and their diameter are in, the ratio 5 : 4, then the ratio of, their height is :, (1) 25 :16, (2) 25 : 64, (3) 64 : 25, (4) 16 : 25, (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 61. The volume of a conical tent is, 1232 cu. m and the area of its, base is 154 sq. m. Find the length, of the canvas required to build the, tent, if the canvas is 2m in width., , FG Take p =, H, (1) 270 m, (3) 276 m, , 22, 7, , IJ, K, (2) 272 m, (4) 275 m, , (SSC Graduate Level Tier-II, Exam. 29.09.2013)

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MENSURATION, 62. If the ratio of the diameters of two, right circular cones of equal height, be 3 : 4, then the ratio of their, volume will be, (1) 3 : 4, (2) 9 : 16, (3) 16 : 9, (4) 27 : 64, , 69. The surface areas of two spheres, are in the ratio 4 : 9. Their volumes will be in the ratio, (1) 2 : 3, (2) 4 :9, (3) 8 : 27, (4) 64 : 729, (SSC Data Entry Operator, Exam. 31.08.2008) & (SSC CHSL, DEO & LDC Exam. 21.10.2012, (IInd Sitting) & (SSC, GL Tier-II Exam. 29.09.2013), , (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 63. A hollow spherical metallic ball has, an external diameter 6 cm and is, 1, cm thick. The volume of the, 2, , FG, H, , 22, ball (in cm3) is Take p = 7, 2, (1) 41, 3, , (3) 47, , 2, 3, , IJ, K, , (4) 40, , 2, 3, , (2) 26, , 1, 3, , 2, , (4) 1 : 3 2, , (SSC CHSL DEO & LDC Exam., 04.11.2012 (IInd Sitting), , 64. The sum of radii of two spheres, is 10 cm and the sum of their, volume is 880 cm3. What will be, the product of their radii ?, , (3) 33, , (3) 1 :, , 2, (2) 37, 3, , (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , (1) 21, , 70. A sphere and a hemisphere have, the same volume. The ratio of their, radii is, (1) 1 : 2, (2) 1 : 8, , 1, 3, , (4) 70, , 71. A solid sphere of 6 cm diameter, is melted and recast into 8 solid, spheres of equal volume. The radi us (in cm) o f each small, sphere is, (1) 1.5, (2) 3, (3) 2, (4) 2.5, (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , 72. The total surface area of a sphere, is 8p square unit. The volume of, the sphere is, , (SSC Section Officer (Commercial Audit), Exam. 25.09.2005), , (1), , 8 2, p cubic unit, 3, , 65. If the radius of a sphere is doubled, its volume becomes, (1) double (2) four times, (3) six times (4) eight times, , (2), , 8, p cubic unit, 3, , (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting), , 66. The radii of two spheres are in, the ratio 3 : 2. Their volume will, be in the ratio :, (1) 9 : 4, (2) 3 : 2, (3) 8 : 27, (4) 27 : 8, (SSC CPO S.I. Exam. 16.12.2007), , 67. The total surface area of a solid, hemisphere is 108p cm2. The volume of the hemisphere is, (1) 72p cm3, (2) 144p cm3, (3) 108 6 cm 3 (4) 54 6 cm3, (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , 68. The largest sphere is carved out, of a cube of side 7 cm. The volume of the sphere (in cm3) will be, (1) 718.66, (2) 543.72, (3) 481.34, (4) 179.67, (SSC CPO S.I. Exam. 06.09.2009), , 8 3, p cubic unit, 5, (SSC Graduate Level Tier-I, Exam. 19.05.2013 Ist Sitting), , 73. Area of the base of a pyramid is, 57 sq.cm. and height is 10 cm,, then its volume (in cm3), is, (1) 570, (3) 190, , (2) 390, (4) 590, FCI Assistant Grade-III, Exam. 25.02.2012 (Paper-I), North Zone (Ist Sitting), , 74. There is a pyramid on a base which, is a regular hexagon of side 2a, cm. If every slant edge of this, pyramid is of length, , (2) 3 2 a3 cm3, , (3) 3 3 a3 cm3 (4) 6a3 cm3, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (North Zone), , 75. The base of a right pyramid is a, square of side 40 cm long. If the, volume of the pyramid is 8000, cm3, then its height is :, (1) 5 cm, (2) 10 cm, (3) 15 cm, (4) 20 cm, (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (Delhi Zone), , 76. The base of a right prism is a trapezium. The length of the parallel, sides are 8 cm and 14 cm and, the distance between the parallel, sides is 8 cm. If the volume of, the prism is 1056 cm3, then the, height of the prism is, (1) 44 cm, (2) 16.5 cm, (3) 12 cm, (4) 10.56 cm, (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (East Zone), , 77. The height of a right prism with, a square base is 15 cm. If the, area of the total surface of the, prism is 608 sq. cm, its volume is, (1) 910 cm3, (2) 920 cm3, 3, (3) 960 cm, (4) 980 cm3, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 78. The base of a right prism is an, equilateral triangle of side 8 cm, and height of the prism is 10 cm., Then the volume of the prism is, (1) 320 3 cubic cm, , (3) 8 3p cubic unit, (4), , (1) 3a3 cm3, , 5a, cm, then, 2, , the volume of this pyramid is, , SME–1142, , (2) 160 3 cubic cm, (3) 150 3 cubic cm, (4) 300 3 cubic cm, (SSC Delhi Police S.I. (SI), Exam. 19.08.2012), , 79. The base of right prism is a triangle whose perimeter is 28 cm and, the inradius of the triangle is 4, cm. If the volume of the prism is, 366 cc, then its height is, (1) 6 cm, (2) 8 cm, (3) 4 cm, (4) None of these, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 80. If the base of a right pyramid is, triangle of sides 5 cm, 12 cm, 13, cm and its volume is 330 cm3 ,, then its height (in cm) will be, (1) 33, (2) 32, (3) 11, (4) 22, (SSC CHSL DEO & LDC Exam., 27.10.2013 IInd Sitting)

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MENSURATION, 81. The diameter of the moon is assumed to be one fourth of the diameter of the earth. Then the ratio of the volume of the earth to, that of the moon is, (1) 64 : 1, (2) 1 : 64, (3) 60 : 7, (4) 7 : 60, (SSC CHSL DEO & LDC Exam., 28.10.2012, Ist Sitting), , 82. A conical vessel whose internal, radius is 12 cm and height 50 cm, is full of liquid. The contents are, emptied into a cylindrical vessel, with radius (internal) 10 cm. The, height to which the liquid rises in, the cylindrical vessel is :, (1) 25cm, (2) 20cm, (3) 24cm, (4) 22cm, (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 83. The volume of a right circular cylinder is equal to the volume of that, right circular cone whose height, is 108 cm and diameter of base, is 30 cm. If the height of the cylinder is 9 cm, the diameter of its, base is, (1) 30 cm, (2) 60 cm, (3) 50 cm, (4) 40 cm, (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone), , 84. The total surface area of a cube, and a sphere are equal. What will, be the ratio between their volume ?, (1) p : 6, , (2), , 6: p, , (3), , p: 6, , (4) 6 : p, , (SSC Section Officer (Commercial, Audit) Exam. 25.09.2005) & (SSC, HSGL Data Entry & LDC, Exam. 28.11.2010 (Ist Sitting) &, (SSC MTS (Non-Technical Staff, Exam. 20.02.2011), , 85. A rectangular paper sheet of dimensions 22 cm × 12 cm is folded in the form of a cylinder along, its length. What will be the volume of this cylinder ? (Take p =, , 22, ), 7, (1) 460 cm, (3) 624 cm3, , 3, , (2) 462 cm, (4) 400 cm3, , 87. The volume of a sphere and a right, circular cylinder having the same, radius are equal , The ratio of the, diameter of the sphere to the, height of the cylinder is, (1) 3 : 2, (2) 2 : 3, (3) 1 : 2, (4) 2 : 1, (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 88. The size of a rectangular piece of, paper is 100 cm × 44 cm. A cylinder is formed by rolling the paper along its length. The volume, of the cylinder is (Use p =, (1) 4400 cm3, (3) 35000 cm3, , (2) 15400 cm3, (4) 144 cm3, , (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 89. A cone, a hemisphere and a cylinder stand on equal bases and, have the same height. The ratio, of their respective volume is, (1) 1 : 2 : 3, (2) 2 : 1 : 3, (3) 1 : 3 : 2, (4) 3 : 1 : 2, Audit) Exam. 30.09.2007 (IInd, Sitting) & (SSC CHSL DEO & LDC, Exam. 11.12.2011 (Delhi Zone) &, (FCI Asst. Grade-III Exam. 25.02.2012, (Paper-I, North Zone, Ist Sitting), , 90. The height of a cylinder and that, of a cone are in the ratio 2 : 3 and, the radii of their bases in the ratio 3 : 4. The ratio of their volume, will be, (1) 1 : 9, (2) 2 : 9, (3) 9 : 8, (4) 3 : 8, (SSC CPO S.I. Exam. 09.11.2008), , 91. Water is flowing at the rate of 5, km/h through a pipe of diameter, 14 cm into a rectangular tank, which is 50 m long, 44m wide., The time taken (in hours) for the, rise in the level of water in the, tank to be 7 cm is, (1) 2, , 1, (2) 1, 2, , (3) 3, , (4) 2, , 86. The ratio of the volume of a cube, to that of a sphere, which will fit, exactly inside the cube, is, (1) p : 6, (2) 6 : p, (3) 3 : p, (4) p : 3, (SSC CGL Prelim Exam. 13.11.2005, (IInd Sitting) & (SSC CGL Prelim, Exam. 27.07.2008 (Ist Sitting), , 1, 2, , (SSC CPO S.I. Exam. 06.09.2009 &, , (SSC CGL Tier-1 Exam. 19.06.2011, (IInd Sitting), , 92. The total surface area of a solid, right circular cylinder is twice that, of a solid sphere. If they have the, same radii, the ratio of the volume of the cylinder to that of the, sphere is given by, , SME–1143, , (2) 2 : 1, (4) 4 : 9, , (SSC CPO (SI, ASI & Intelligence Officer), Exam. 28.08.2011 (Paper-I), , 93. In a cylindrical vessel of diameter, 24 cm filled up with sufficient, quantity of water, a solid spherical ball of radius 6 cm is completely immersed. Then the increase in height of water level is :, (1) 1.5 cm, (2) 2 cm, (3) 3 cm, (4) 4.2 cm, FCI Assistant Grade-III, Exam. 05.02.2012 (Paper-I), East Zone (IInd Sitting), , 94. A solid wooden toy is in the shape, of a right circular cone mounted, on a hemisphere. If the radius of, the hemisphere is 4.2 cm and the, total height of the toy is 10.2 cm,, find the volume of the wooden toy, (nearly)., (1) 104 cm3, (2) 162 cm3, (3) 427 cm3, (4) 266 cm3, FCI Assistant Grade-III, Exam. 05.02.2012 (Paper-I), East Zone (IInd Sitting), , (SSC Section Officer (Commercial, , 3, , (SSC Section Officer (Commercial Audit), Exam. 25.09.2005), , 22, ), 7, , (1) 9 : 4, (3) 3 : 1, , 95. The respective height and volume, of a hemisphere and a right circular cylinder are equal, then the, ratio of their radii is, (1), , 2 :, , (3), , 3 :, , 3, 2, , (2), , 3 :1, , (4) 2 :, , 3, , (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (North Zone), , 96. The ratio of the volume of a cube, and of a solid sphere is 363 : 49., The ratio of an edge of the cube, and the radius of the sphere is, (taking p =, , 22, ), 7, , (1) 7 : 11, (3) 11 : 7, , (2) 22 : 7, (4) 7: 22, , (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (East Zone), , 97. From a right circular cylinder of, radius 10 cm and height 21 cm,, a right circular cone of same baseradius is removed. If the volume, of the remaining portion is 4400, cm3, then the height of the removed cone (taking p =, (1) 15 cm, (3) 21 cm, , 22, ) is :, 7, , (2) 18 cm, (4) 24 cm, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (Delhi Zone)

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MENSURATION, 98. If a solid cone of volume 27 p cm, is kept inside a hollow cylinder, whose radius and height are that, of the cone, then the volume of, water needed to fill the empty, space is, (1) 3p cm3, (2) 18 p cm3, (3) 54 p cm3, (4) 8l p cm3, 3, , (SSC Graduate Level Tier-II, Exam.16.09.2012), , 99. A cylindrical can whose base is, horizontal and is of internal radius 3.5 cm contains sufficient water so that when a solid sphere, is placed inside, water just covers the sphere. The sphere fits, in the can exactly. The depth of, water in the can before the, sphere was put, is, (1), , (3), , 35, cm, 3, , (2), , 17, cm, 3, , 7, cm, 3, , 14, (4), cm, 3, , (SSC Graduate Level Tier-II, Exam.16.09.2012), , 100. If A denotes the volume of a right, circular cylinder of same height, as its diameter and B is the volume of a sphere of same radius,, then, , A, is :, B, , (1), , 4, 3, , (2), , 3, 2, , (3), , 2, 3, , (4), , 3, 4, , (SSC CHSL DEO & LDC, Exam. 21.10.2012 (IInd Sitting), , 101. The base of a right circular cone, has the same radius a as that of, a sphere. Both the sphere and the, cone have the same volume., Height of the cone is, (1) 3a, (2) 4a, (3), , 7, a, 4, , (4), , 7, a, 3, , (SSC CHSL DEO & LDC, Exam. 28.10.2012 (Ist Sitting), , (1), , 3: 2, , (2) 3 3 : 2, , (3), , 3:2 2, , (4), , 2: 6, , (SSC Graduate Level Tier-I, Exam. 11.11.2012, Ist Sitting), , 103. A semicircular sheet of metal of, diameter 28 cm is bent into an, open conical cup. The capacity, , 22, ) is, 7, (2) 622.38 cm3, (4) 623.20 cm3, , of the cup (taking p =, (1) 624.26 cm3, (3) 622.56 cm3, , (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , 104. A conical flask is full of water. The, flask has base radius r and height, h. This water is poured into a, cylindrical flask of base radius m., The height of water in the, cylindrical flask is, , m, (1), 2h, (3), , h 2, m, (2), 2, , 2h, m, , h, , (4), , 3m 2, , (SSC Graduate Level Tier-I, Exam. 19.05.2013 Ist Sitting), , 105. The volume of a cylinder and a, cone are in the ratio 3 : 1. Find, their diameters and then compare, them when their heights are, equal., (1) Diameter of cylinder = 2 times, of diameter of cone, (2) Diameter of cylinder = Diameter of cone, (3) Diameter of cylinder > Diameter of cone, (4) Diameter of cylinder < Diameter of cone, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 106. A cone of height 7 cm and base, radius 1 cm is carved from a, cuboidal block of wood 10 cm ×, , 22, 5cm × 2 cm. [Assuming p =, ], 7, The percentage wood wasted in, the process is :, , 102. The radii of the base of a cylinder and a cone are in the, , (1) 92, , 2, %, 3, , (2) 46, , 1, %, 3, , ratio 3 : 2 and their heights, , (3) 53, , (4) 7, , are in the ratio 2 : 3 . Their, volume are in the ratio of, , 2, %, 3, , (SSC CGL Prelim Exam. 24.02.2002, (Second Sitting), , 1, %, 3, , SME–1144, , 107. If the radius of a cylinder is decreased by 50% and the height, is increased by 50% to form a, new cylinder, the volume will be, decreased by, (1) 0%, (2) 25%, (3) 62.5%, (4) 75%, (SSC CPO S.I. Exam. 07.09.2003), , 108. Each of the height and base-radius of a cone is increased by, 100%. The percentage increase, in the volume of the cone is, (1) 700%, (2) 400%, (3) 300%, (4) 100%, (SSC CPO S.I. Exam. 07.09.2003), , 109. If both the radius and height of, a right circular cone are increased by 20%, its volume will, be increased by, (1) 20%, (2) 40%, (3) 60%, (4) 72.8%, (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 110. If the height of a right circular, cone is increased by 200% and, the radius of the base is reduced, by 50%, the volume of the cone, (1) increases by 25%, (2) increases by 50%, (3) remains unaltered, (4) decreases by 25%, (SSC CPO S.I. Exam. 03.09.2006), , 111. If the height and the radius of, the base of a cone are each increased by 100%, then the volume of the cone becomes, (1) double that of the original, (2) three times that of the original, (3) six times that of the original, (4) eight times that of the original, (SSC CPO S.I. Exam. 03.09.2006), , 112. If the radius of a right circular, cylinder is decreased by 50% and, its height is increased by 60%,, its volume will be decreased by, (1) 10%, (2) 60%, (3) 40%, (4) 20%, (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting), , 113. The length, breadth and height, of a cuboid are in the ratio, 1 : 2 : 3. If they are increased by, 100%, 200% and 200% respectively, then compared to the original volume the increase in the, volume of the cuboid will be, (1) 5 times, (2) 18 times, (3) 12 times, (4) 17 times, (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting)

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MENSURATION, 114. Each of the radius of the base, and the height of a right circular, cylinder is increased by 10%. The, volume of the cylinder is increased by, (1) 3.31%, (2) 14.5%, (3) 33.1%, (4) 19.5%, , of the prism is 20 cm. The density of the material of the prism, is 6 gm/cubic cm. The weight of, the prism is, (1) 6.4 kg, (2) 7.2 kg, (3) 3.4 kg, (4) 4.8 kg, (SSC CHSL DEO & LDC Exam., 21.10.2012 (Ist Sitting), , (SSC CPO S.I. Exam. 09.11.2008), , & (SSC SAS Exam. 26.06.2010, (Paper-I), , 115- If the height of a cone is increased, by 100% then its volume is increased by :, (1) 100%, (2) 200%, (3) 300%, (4) 400%, (SSC CHSL DEO & LDC, Exam. 27.11.2010), , 116. A hemispherical cup of radius 4, cm is filled to the brim with coffee. The coffee is then poured into, a vertical cone of radius 8 cm and, height 16 cm. The percentage of, the volume of the cone that remains empty is :, (1) 87.5%, (2) 80.5%, (3) 81.6%, (4) 88.2%, (SSC CHSL DEO & LDC Exam., 21.10.2012 (IInd Sitting), , 117. The volume (in m3) of rain water, that can be collected from 1.5, hectares of ground in a rainfall, of 5 cm is, (1) 75, , (2) 750, , (3) 7500, , (4) 75000, , (SSC CGL Tier-1 Exam. 26.06.2011, (First Sitting), , 118. Each edge of a regular tetrahedron is 3 cm, then its volume is, (1), , 9 2, c.c., 4, , (2) 27 3 c.c., , (3), , 4 2, c.c., 9, , (4) 9 3 c.c., , (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (North Zone), , 119. The perimeter of the triangular, base of a right prism is 15 cm, and radius of the incircle of the, triangular base is 3 cm. If the, volume of the prism be 270 cm3,, then the height of the prism is, (1) 6 cm, (2) 7·5 cm, (3) 10 cm, (4) 12 cm, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (East Zone), , 120. A prism has as the base a rightangled triangle whose sides adjacent to the right angles are 10, cm and 12 cm long. The height, , 121. A copper rod of 1 cm diameter, and 8 cm length is drawn into a, wire of uniform diameter and 18, m length. The radius (in cm) of, the wire is, (1), , 1, 15, , (2), , 1, 30, , (3), , 2, 15, , (4) 15, , (SSC CGL Prelim Exam. 13.11.2005, (Second Sitting), , 122. A well 20 m in diameter is dug, 14 m deep and the earth taken, out is spread all around it to a, width of 5 m to form an, embankment. The height of the, embankment is :, (1) 10 m, (2) 11 m, (3) 11.2 m, (4) 11.5 m, (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 123. Two solid cylinders of radii 4 cm, and 5cm and length 6 cm and 4, cm respectively are recast into, cylindrical disc of thickness1 cm., The radius of the disc is, (1) 7 cm, (2) 14 cm, (3) 21 cm, (4) 28 cm, (SSC CPO S.I. Exam. 06.09.2009), , 124. A metallic hemisphere is melted, and recast in the shape of a cone, with the same base radius (R) as, that of the hemisphere. If H is, the height of the cone, then :, , 2, R, 3, , (1) H = 2R, , (2) H =, , (3) H =, , (4) B = 3R, , 3R, , (SSC CGL Prelim Exam. 04.07.1999, (First Sitting), , 125. Three solid metallic spheres of, diameter 6 cm, 8 cm and 10 cm, are melted and recast into a new, solid sphere. The diameter of the, new sphere is :, (1) 4 cm, (2) 6 cm, (3) 8 cm, (4) 12 cm, (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 126. Three solid metallic balls of radii 3 cm, 4 cm and 5 cm are, melted and moulded into a single, solid ball. The radius of the new, ball is :, , SME–1145, , (1) 2 cm, (3) 4 cm, , (2) 3 cm, (4) 6 cm, , (SSC CGL Prelim Exam. 24.02.2002, (Second Sitting), , 127. Three solid spheres of a metal, whose radii are 1 cm, 6 cm and, 8 cm are melted to form an other, solid sphere. The radius of this, new sphere is, (1) 10.5 cm (2) 9.5 cm, (3) 10 cm, (4) 9 cm, (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone), , 128. A sphere of radius 2 cm is put, into water contained in a cylinder of base-radius 4 cm. If the, sphere is completely immersed, in the water, the water level in, the cylinder rises by, (1), , 1, cm, 3, , (2), , 1, cm, 2, , (3), , 2, cm, 3, , (4) 2 cm, , (SSC CPO S.I. Exam. 07.09.2003), , 129. 12 spheres of the same size are, made by melting a solid cylinder, of 16 cm diameter and 2 cm, height. The diameter of each, sphere is :, (1) 2 cm, (2) 4 cm, (3) 3 cm, , (4), , 3 cm, , (SSC CGL Prelim Exam. 13.11.2005, (First Sitting), , 130. By melting a solid lead sphere of, diameter 12 cm, three small, spheres are made whose diameters are in the ratio 3 : 4 : 5., The radius (in cm) of the smallest sphere is, (1) 3, (2) 6, (3) 1.5, (4) 4, (SSC CGL Prelim Exam. 13.11.2005, (Second Sitting), , 131. A solid metallic sphere of radius, 3 decimetres is melted to form a, circular sheet of 1 milimetre, thickness. The diameter of the, sheet so formed is, (1) 26 metres (2) 24 metres, (3) 12 metres (4) 6 metres, (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 132. A copper wire of Iength 36 m and, diameter 2 mm is melted to form, a sphere. The radi us of the, sphere (in cm) is, (1) 2.5, (2) 3, (3) 3.5, (4) 4, (SSC CGL Tier-I Exam. 16.05.2010, (Second Sitting)

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MENSURATION, 133. A child reshapes a cone made up, of clay of height 24cm and radius, 6cm into a sphere. The radius (in, cm) of the sphere is, (1) 6, (2) 12, (3) 24, (4) 48, (SSC CGL Tier-1 Exam. 19.06.2011, (First Sitting), , 134. A solid metallic spherical ball of, diameter 6 cm is melted and, recasted into a cone with diameter of the base as 12 cm. The, height of the cone is, (1) 6 cm, (2) 2 cm, (3) 4 cm, (4) 3 cm, (SSC CPO S.I. Exam. 12.01.2003), , 135. The diameter of the iron ball, used for the shot-put game is 14, cm. It is melted and then a solid, , 1, cm is, 3, made. What will be the diameter, of the base of the cylinder ?, (1) 14 cm, (2) 28 cm, , cylinder of height 2, , (3), , 14, cm, 3, , (4), , 28, cm, 3, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 136. The radius of the base and height, of a metallic solid cylinder are r, cm and 6 cm respectively. It is, melted and recast into a solid, cone of the same radius of base,, The height of the cone is :, (1) 54 cm, (2) 27 cm, (3) 18 cm, (4) 9 cm, (SSC CPO S.I. Exam. 16.12.2007), , 137. A solid metallic cone is melted, and recast into a solid cylinder, of the same base as that of the, cone. If the height of the cylinder is 7cm, the height of the cone, was, (1) 20 cm, (2) 21 cm, (3) 28 cm, (4) 24 cm, (SSC Data Entry Operator, Exam. 02.08.2009), , 138. A solid spherical copper ball,, whose diameter is 14 cm, is, melted and converted into a wire, having diameter equal to 14 cm., The length of the wire is, (1) 27 cm, , 16, (2), cm, 3, , (3) 15 cm, , (4), , 28, cm, 3, , (SSC Constable (GD), Exam. 12.05.2013 Ist Sitting), , 139. A solid sphere is melted and, recast into a right circular cone, with a base radius equal to the, radius of sphere. What is the ratio, of the height and radius of the, cone so formed?, (1) 4:3, (2) 2:3, (3) 3 : 4, (4) 4 :1, (SSC Constable (GD), Exam. 12.05.2013), , 140. A sphere of diameter 6 cm is, dropp ed i n a right circular, cylindrical vessel partly filled with, water. The diameter of the, cylindrical vessel is 12 cm. If the, sphere i s j u st compl etel y, submerged in water, then the rise, of water level in the cylindrical, vessel is, (1) 2 cm, (2) 1 cm, (3) 3 cm, (4) 4 cm, (SSC Graduate Level Tier-I, Exam. 19.05.2013), , 141. A copper sphere of diameter 18, cm is drawn into a wire of diameter 4 mm. The length of the wire,, in metre, is :, (1) 2.43, (2) 243, (3) 2430, (4) 24.3, (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 142. A rectangular block of metal has, dimensions 21 cm, 77 cm and 24, cm. The block has been melted, into a sphere. The radius of the, sphere is, , FG Take p, H, , (1) 21 cm, (3) 14 cm, , =, , 22, 7, , IJ, K, , (2) 7 cm, (4) 28 cm, , (SSC Graduate Level Tier-II, Exam. 29.09.2013, , 143. The radius of cross-section of a, solid cylindrical rod of iron is 50, cm. The cylinder is melted down, and formed into 6 solid spherical, balls of the same radius as that, of the cylinder. The length of the, rod (in metres) is, (1) 0.8, (2) 2, (3) 3, (4) 4, (SSC CHSL DEO & LDC Exam., 27.10.2013 IInd Sitting), , 144. Two right circular cones of equal, height of radii of base 3 cm and, 4 cm are melted together and, made to a solid sphere of radius, 5 cm. The height of a cone is, (1) 10 cm, (2) 20 cm, (3) 30 cm, (4) 40 cm, (SSC CHSL DEO & LDC Exam., 27.10.2013 IInd Sitting), , SME–1146, , 145. A tank 40 m long, 30 m broad, and 12 m deep is dug in a field, 1000 m long and 30 m wide. By, how much will the level of the field, rise if the earth dug out of the, tank is evenly spread over the, field ?, (1) 2 metre, (2) 1.2 metre, (3) 0.5 metre, (4) 5 metre, (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , 146. A right pyramid 6 m hight has a, square base of which the diagonal is 1152 m. Volume of the, pyramid is, (1) 144 m3, (2) 288 m3, (3) 576 m3, (4) 1152 m3, (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , 147. If the ratio of volumes of two, cones is 2 : 3 and the ratio of the, radii of their bases is 1 : 2, then, the ratio of their heights will be, (1) 8 : 3, (2) 3 : 8, (3) 4 : 3, (4) 3 : 4, (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , 148. Two cubes have their volumes in, the ratio 27 : 64. The ratio of their, surface areas is, (1) 9 : 25, (2) 16 : 25, (3) 9 : 16, (4) 4 : 9, (SSC CGL Tier-I Re-Exam. (2013), 20.07.2014 (Ist Sitting), , 149. The radius of the base and the, height of a right circular cone are, doubled. The volume of the cone, will be, (1) 8 times of the previous volume, (2) three times of the previous, volume, (3) 3 2 times of the previous, volume, (4) 6 times of the previous volume, , (SSC CGL Tier-I Re-Exam. (2013), , 20.07.2014 (IInd Sitting), , 150. The ratio of weights of two, spheres of different materials is, 8 : 17 and the ratio of weights, per 1 cc of materials of each is, 289 : 64. The ratio of radii of the, two spheres is, (1) 8 : 17, (2) 4 : 17, (3) 17 : 4, (4) 17 : 8, (SSC CGL Tier-I Re-Exam. (2013), , 20.07.2014 (IInd Sitting), , 151. Three cubes of sides 6 cm, 8 cm, and 1 cm are melted to form a, new cube. The surface area of, the new cube is, (1) 486 cm2, (2) 496 cm2, (3) 586 cm2, (4) 658 cm2, (SSC CGL Tier-I Re-Exam. (2013), , 20.07.2014 (IInd Sitting)

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MENSURATION, 152. A sphere is cut into two hemispheres. One of them is used as, bowl. It takes 8 bowlfuls of this, to fill a conical vessel of height, 12 cm and radius 6 cm. The radius of the sphere (in centimetre) will be, (1) 3, (2) 2, (3) 4, (4) 6, (SSC CGL Tier-I Exam., 19.10.2014 (Ist Sitting), , 153. The volumes of a right circular, cylinder and a sphere are equal., The radius of the cylinder and, the diameter of the sphere are, equal. The ratio of height and, radius of the cylinder is, (1) 3 : 1, (2) 1 : 3, (3) 6 : 1, (4) 1 : 6, (SSC CGL Tier-I Exam. 19.10.2014), , 154. Some bricks are arranged in an, area measuring 20 cu. m. If the, length, breadth and height of, each brick is 25 cm, 12.5 cm, and 8 cm respectively, then in, that pile the number of bricks, are (suppose there is no gap in, between two bricks), (1) 6,000, (2) 8,000, (3) 4,000, , (4) 10,000, , (SSC CGL Tier-I Exam. 26.10.2014), , 155. The height of a cone is 30 cm. A, small cone is cut off at the top, by a plane parallel to the base., 1, If its volume be, th of the vol27, ume of the given cone, at what, height above the base is the section made ?, (1) 19 cm, (2) 20 cm, (3) 12 cm, (4) 15 cm, (SSC CGL Tier-II Exam. 21.09.2014), , 156. The height of the right pyramid, whose area of the base is 30 m2, and volume is 500 m3, is, (1) 50 m, (2) 60 m, (3) 40 m, (4) 20 m, (SSC CGL Tier-II Exam. 21.09.2014), , 157. The base of a right prism is an, equilateral triangle. If the lateral, surface area and volume is 120, , 3, , 2 = 1.259] is approximately, (1) 5.038 cm (2) 5.190 cm, (3) 1.038 cm (4) 0.518 cm, (SSC CGL Tier-II Exam. 21.09.2014), , 159. A large solid sphere is melted and, moulded to form identical right, circular cones with base radius, and height same as the radius, of the sphere. One of these, cones is melted and moulded to, form a smaller solid sphere. Then, the ratio of the surface area of, the smaller to the surface area, of the larger sphere is, 4, , 3, , (1) 1 : 3 3, , (2) 1 : 2 2, , 2, , 4, , (3) 1 : 3 3, , (4) 1 : 2 3, , LM, N, , (SSC CGL Tier-II Exam. 21.09.2014), , 158. A ball of lead 4 cm in diameter is, covered with gold. If the volume, of the gold and lead are equal,, then the thickness of gold [given, , radius of the base of the circular, cone. Then the height of the water in the cylindrical flask is, (1) 32 cm, (2) 24 cm, (3) 48 cm, (4) 72 cm, (SSC CHSL DEO & LDC, Exam. 9.11.2014), , 164. The whole surface of a cube is, 150 sq.cm. Then the volume of, the cube is, (1) 125 cm3, (2) 216 cm3, (3) 343 cm3, (4) 512 cm3, Exam. 16.11.2014), , (SSC CGL Tier-II Exam. 21.09.2014), , ume of the ice-cream is p =, , 22, 7, , OP, Q, , (1) 1078 cubic cm, (2) 1708 cubic cm, (3) 7108 cubic cm, , 165. A solid metallic spherical ball of, diameter 6 cm is melted and recast into a cone with diameter of, the base as 12 cm. The height of, the cone is, (1) 2 cm, (2) 3 cm, (3) 4 cm, (4) 6 cm, (SSC CHSL DEO & LDC, Exam. 16.11.2014), , 166. A hemispherical bowl of internal, radius 15 cm contains a liquid., The liquid is to be filled into cylindrical shaped bottles of diameter 5 cm and height 6 cm. The, number of bottles required to, empty the bowl is, (1) 30, (2) 40, (3) 50, (4) 60, (SSC CHSL DEO & LDC, , (4) 7180 cubic cm, (SSC CGL Tier-II Exam. 21.09.2014), , 161. A hollow sphere of internal and, external diameters 6 cm and 10, cm respectively is melted into a, right circular cone of diameter 8, cm. The height of the cone is, (1) 22.5 cm, (2) 23.5 cm, (3) 24.5 cm, (4) 25.5 cm, , Exam. 16.11.2014), , 167. If V1, V2 and V3 be the volumes, of a right circular cone, a sphere, and a right circular cylinder having the same radius and same, height, then, (1) V1 =, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014), , 162. Each edge of a regular tetrahedron is 4 cm. Its volume (in cubic cm) is, (1), , 16 3, 3, , (2) 16 3, , (3), , 16 2, 3, , (4) 16 2, , 1, rd of, 3, , (SSC CHSL DEO & LDC, , 160. A conical cup is filled with icecream. The ice-cream forms a, hemispherical shape on its open, top. The height of the hemispherical part is 7 cm. The radius of, the hemispherical part equals the, height of the cone. Then the vol-, , cm 2], , 3, 40 3 cm respectively, then the side of base of the prism is, (1) 4 cm, (2) 5 cm, (3) 7 cm, (4) 40 cm, , cal flask whose radius is, , V2, V3, =, 2, 3, , (2), , V1, V2, =, = V3, 2, 3, , (3), , V1, V2, =, = V3, 3, 2, , (4), , V1, V3, = V2 =, 3, 2, , (SSC CHSL DEO Exam. 02.11.2014, , (SSC CHSL DEO & LDC Exam., 02.11.2014 (IInd Sitting), , 163. A flask in the shape of a right, circular cone of height 24 cm is, filled with water. The water is, poured in right circular cylindri-, , SME–1147, , (Ist Sitting), , 168. If the radius of a shphere be doubled, then the percentage increase in volume is, (1) 500%, (2) 700%, (3) 600%, (4) 800%, (SSC CHSL DEO Exam. 16.11.2014, (Ist Sitting)

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MENSURATION, 169. If 64 buckets of water are removed from a cubical shaped, water tank completely filled with, , 1, of the tank remains, 3, , water,, , filled with water. The length of, each side of the tank is 1.2 m., Assuming that all buckets are of, the same measure, then the volume (in litres) of water contained, by each bucket is, (1) 12, (2)16, (3) 15, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 170. A wooden box of dimensions 8, metre × 7 metre × 6 metre is to, carry rectangular boxes of dimensions 8 cm × 7 cm × 6 cm. The, maximum number of boxes that, can be carried in 1 wooden box is, (1) 7500000, (2) 9800000, (3) 1200000, (4) 1000000, (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam. 22.06.2014, TF No. 999 KP0), , 171. Two circular cylinders of equal, volume have their heights in the, ratio 1 : 2. Ratio of their radii is, , 22, (Take p =, ), 7, (2) 1 :, , (3), , (4) 1 : 2, , 2, , (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam. 22.06.2014, TF No. 999 KP0), , 172. A rectangular piece of paper of, dimensions 22 cm by 12 cm is, rolled along its length to form a, cylinder. The volume (in cu.cm.), of the cylinder so formed is ( use, , 22, p =, ), 7, (2) 412, (4) 362, , (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam. 22.06.2014, TF No. 999 KP0), , 173. A sphere is placed inside a right, circular cylinder so as to touch, the top, base and the lateral surface of the cylinder. If the radius, of the sphere is R, the volume of, the cylinder is, (1) 2pR3, (2) 4pR3, (3) 8pR3, , (3), , 4 8, 4 60, cm3 (2), cm3, 3, 3, 4 61, 4 59, cm3 (4), cm3, 3, 3, , (SSC CGL Tier-I Exam. 19.10.2014, , 175. If the radius of the base of a cone, be 7 cm and its curved surface, area be 550 sq. cm, then the volume of the cone is, (1) 1232 cu. cm (2) 1024 cu. cm, (3) 1132 cu. cm (4) 1324 cu. cm, (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014 , Ist Sitting, TF No. 333 LO 2), , 176. A hemisphere of iron is melted, and recast in the shape of a right, circular cylinder of diameter 18, cm and height 162 cm. The radius of the hemisphere is, (1) 27 cm, (2) 9 cm, (3) 6 cm, (4) 12 cm, (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , (1) 1 : 4, , (1) 562, (3) 462, , (1), , TF No. 022 MH 3), , (4) 18, , 2 :1, , 174. The base of a right pyramid is, an equilateral triangle of side 4, cm each. Each slant edge is 5, cm long. The volume of the pyramid is, , (4), , 8, pR3, 3, , (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam. 22.06.2014, TF No. 999 KP0), , 177. An iron sphere of radius 27 cm, is melted to form a wire of length, 729 cm. The radius of wire is, (1) 6 cm, (2) 9 cm, (3) 18 cm, (3) 36 cm, (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , 178. A right circular cylinder is circumscribed about a hemisphere so, that they share the same base., The ratio of the volumes of cylinder and hemisphere is, (1) 4 : 3, (2) 3 : 1, (3) 3 : 4, (4) 3 : 2, (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , 179. The ratio of volumes of two cubes, is 8 : 125. The ratio of their surface areas is, (1) 4 : 25, (2) 2 : 75, (3) 2 : 15, (4) 4 : 15, (SSC CHSL (10+2) DEO & LDC, , Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , 180. A spherical ball of radius 1 cm is, dropped into a conical vessel of, radius 3 cm and slant height 6, cm. The volume of water (in cm3),, that can just immerse the ball, is, , SME–1148, , 5p, 3, , (2), , p, 3, , (3) 3 p, , (4), , 4p, 3, , (1), , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 181. Assume that a drop of water is, spherical and its diameter is onetenth of a cm. A conical glass has, a height equal to the diameter of, its rim. If 32000 drops of water, fill the glass completely, then the, height of the glass (in cm.) is, (1) 3, (2) 1, (3) 4, , (4) 2, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 182. If the height of a cylinder is 4, times its circumference, the volume of the cylinder in terms of, its circumference c, is, (1), , 2c3, p, , (2) 4pc3, , (3), , c3, p, , (4) 2pc3, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 183. Base of a right pyramid is a, square whose area is 324 sq, metre. If the volume of the pyramid is 1296 cu.metre, then the, area (in sq. metre) of the slant, surface is, (1) 432, (2) 540, (3) 1080, (4) 360, (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 184. If the surface areas of two, spheres are in the ratio 9 : 16,, the ratio of their volumes is, (1) 16 : 9, (2) 27 : 64, (3) 64 : 27, (4) 9 : 16, (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 185. The volume of a right circular cone, is equal to the volume of a right, circular cylinder. The height and, the radius of the cylinder are 9, cm and 20 cm respectively. If the, height of the cone is 108 cm, then, its radius, (in cm) is, (1) 12, (3) 20, , (2) 14, (4) 10, (SSC CGL Tier-II Exam,, , 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7)

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MENSURATION, 186. A right circular cone and a right, circular cylinder have the same, base and their heights are in the, ratio 2 : 3. The ratio of their volumes will be, (1) 1 : 9, (3) 5 : 9, , (2) 4 : 9, (4) 2 : 9, , (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 187. A cone, a cylinder and a hemisphere stand on equal bases and, have equal heights. The ratio of, their volumes is, (1) 2 : 3 : 1, , (2) 2 : 1 : 3, , (3) 1 : 3 : 2, , (4) 1 : 2 : 3, , (SSC CGL Tier-II Exam,, , 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 188. The diameters of the internal and, external surfaces of a hollow, spherical shell are 6 cm and 10, cm respectively. If it is melted, , 8, and a solid cylinder of length, 3, cm is made, then the diameter, (in cm) of the cylinder is, (1) 10, (2) 14, (3) 16, (4) 7, (SSC CGL Tier-II Exam,, , 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 189. The volume of a metallic cylindrical pipe is 748 cm3. Its length is, 14 cm and external radius is 9, cm. Its thickness is, (Use p =, , 22, 7, , (1) 1 cm, (3) 17 cm, , ), (2) 7 cm, (4) 11 cm, , (SSC CGL Tier-II Exam,, , 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 190. A cylindrical vessel of diameter, 24 cm contains some water. If, two spheres of radii 6 cm each, are lowered into the water until, they are completely immersed,, then the water level (in cm) in the, vessel will rise by, (1) 12, (3) 4, , (2) 6, (4) 9, , (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 191. The perimeter of one face of a, cube is 20 cm. Its volume will be, (1) 625 cm3, (3) 125 cm3, , (2) 100 cm3, (4) 400 cm3, , (SSC CGL Tier-I Exam, 09.08.2015, (Ist Sitting) TF No. 1443088), , 192. If the volume of a sphere is numerically equal to its surface area, then its diameter is, (1) 6 cm, (2) 4 cm, (3) 2 cm, (4) 3 cm, , (1), , 1, Part, 4, , (2), , 1, Part, 2, , (3), , 2, Part, 9, , (4), , 1, Part, 9, , (SSC CGL Tier-I Exam, 16.08.2015, , (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , (Ist Sitting) TF No. 3196279), , 193. A conical iron piece having diameter 28 cm and height 30cm is, totally immersed into the water, of a cylindrical vessel, resulting, in the rise of water level by 6.4, cm. The diameter, in cm, of the, vessel is :, (1) 3.5, , 35, (2), 2, , (3) 32, , (4) 35, , (SSC CGL Tier-I Exam, 16.08.2015, (IInd Sitting) TF No. 2176783), , 194. A solid right prism made of iron, has cross section of a triangle of, sides 5cm, 10cm, 13cm and of, height 10 cm. If one cubic cm of, iron weights 7g, then the weight, of the prism is (approximately), (1) 1570.8 gram, (2) 1371.32 gram, (3) 1470.8 gram, (4) 1100.68 gram, (SSC Constable (GD), Exam, 04.10.2015, Ist Sitting), , 195. A right circular cone of height 20, cm and base radius 15 cm is, melted and cast into smaller, cones of equal sizes of height 5, cm and base radius 1.5 cm. The, number of cones cast are, (1) 300, (2) 150, (3) 400, (4) 100, (SSC Constable (GD), Exam, 04.10.2015, Ist Sitting), , 196. A right prism has a triangular, base whose sides are 13 cm, 20, cm and 21 cm. If the altitude of, the prism is 9 cm, then its volume is, (1) 1314 cm3 (2) 1134 cm3, (3) 1413 cm3 (4) 1143 cm3, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 197. The portion of a ditch 48m long,, 16.5 m wide and 4 m deep that, can be filled with stones and earth, available during excavation of a, tunnel, cylindrical in shape, of diameter 4 m and length 56 m is, , FG Take p = 22 IJ, H, 7 K, , SME–1149, , 198. If a hemisphere is melted and, four spheres of equal volume are, made, the radius of each sphere, will be equal to, (1), , 1, th of the radius of the, 4, , hemisphere, (2) radius of the hemisphere, (3), , 1, o f the radius of the, 2, hemisphere, , 1, (4), th of the radius of the, 6, hemisphere, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 199. A cylinder with base radius 8 cm, and height 2 cm is melted to form, a cone of height 6 cm. The radius of the cone will be, (1) 6 cm, (2) 8 cm, (3) 4 cm, (4), 5 cm, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 200. A plane divides a right circular, cone into two parts of equal, volume. If the plane is parallel to, the base, then the ratio, in which, the height of the cone is divided, is, (1) 1 : 3 2, , (2) 1 : 2, , (3) 1 : 3 2 + 1 (4) 1 : 3 2 – 1, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 201. The radii of two solid iron spheres, are 1 cm and 6 cm respectively., A hollow sphere is made by melting, the two spheres. If the external, radius of the hollow sphere is 9, cm, then its thickness (in cm) is, (1) 2, (2), 1.5, (3) 0.5, (4), 1, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 202. The base of a right prism is a trapezium whose lengths of two parallel sides are 10 cm and 6 cm, and distance between them is 5, cm. If the height of the prism is, 8 cm, its volume is, (1) 320 cm3, (2) 300.5 cm3, (3) 310 cm3, (4) 300 cm3, (SSC CHSL (10+2) LDC, DEO & PA/SA, Exam, 01.11.2015, IInd Sitting)

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MENSURATION, 203. The radius of a hemispherical, bowl is 6 cm. The capacity of the, bowl is, (Take p =, , 22, ), 7, , (1) 345.53 cm3(2) 452 cm3, (3) 495.51 cm3(4) 452.57 cm3, 204. Length of each edge of a regular, tetrahedron is 1 cm. Its volume, is :, (1), , 3, cu. cm., 12, , 1, (2), 4, (3), , (4), , 3 cu. cm., , 2, cu. cm., 6, , 1, 12, , 2 cu. cm., , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (IInd Sitting) TF No. 7203752), , 205. The volume of a right circular cone, which is obtained from a wooden, cube of edge 4.2 dm wasting, minimum amount of word is :, (1) 19404 cu. dm, (2) 194.04 cu. dm, (3) 19.404 cu. dm, (4) 1940.4 cu. dm, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (IInd Sitting) TF No. 7203752), , 206. Base of a right prism is a rectangle, the ratio of whose length and, breadth is 3 : 2. If the height of, the prism is 12 cm and total surface area is 288 sq. cm., the volume of the prism is :, (1) 291 cm3, (2) 288 cm3, 3, (3) 290 cm, (4) 286 cm3, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (IInd Sitting) TF No. 7203752), , 207. A right triangle with sides 9 cm,, 12 cm and 15 cm is rotated about, the side of 9 cm to form a cone., The volume of the cone so formed, is :, (1) 327 p cm3 (2) 330 p cm3, (3) 334 p cm3 (4) 324 p cm3, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (Ist Sitting) TF No. 1375232), , 208. Volume of a right circular cylinder of height 21 cm and base, radius 5 cm is :, (1) 1255 cm3, (2) 1050 cm3, 3, (3) 1175 cm, (4) 1650 cm3, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (Ist Sitting) TF No. 1375232), , 209. The volume of the largest right, circular cone that can be cut out, of a cube of edge 7 cm ?, , FG Use p = 22 IJ, H, 7 K, (1) 121 cm3, (3) 13-6 cm3, , FG Take p = 22 IJ, H, 7 K, (1) 1760, (3) 220, , (2) 440, (4) 880, (SSC CGL Tier-II Online, Exam.01.12.2016), , (2) 89-8 cm3, (4) 147-68 cm3, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (IInd Sitting) TF No. 3441135), , 210. By melting two solid metallic, spheres of radii 1 cm and 6 cm,, a hollow sphere of thickness 1, cm is made. The external radius, of the hollow sphere will be, (1) 9 cm, (2) 6 cm, (3) 7 cm, (4) 8 cm, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 20.12.2015, (Ist Sitting) TF No. 9692918), , 211. Height of a prism–shaped part of, a machine is 8 cm and its base is, an isosceles triangle, whose each, of the equal sides is 5 cm and, remaining side is 6 cm. The, volume of the part is, (1) 96 cu. cm (2) 120 cu. cm, (3) 86 cu. cm (4) 90 cu. cm, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 20.12.2015, (Ist Sitting) TF No. 9692918), , 212. A cuboidal shaped water tank,, 2.1 m long and 1.5 m broad is, half filled with water. If 630 litres, more water is poured into that, tank, the water level will rise, (1) 0.15 cm, (2) 0.20 metre, (3) 0.18 cm, , 214. A hollow cylindrical tube 20 cm., long is made of iron and its external and internal diameters are, 8 cm. and 6 cm. respectively. The, volume (in cubic cm.) of iron used, in making the tube is, , (4) 2 cm, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 20.12.2015, (Ist Sitting) TF No. 9692918), , 213. A solid sphere of radius 9 cm is, melted to form a sphere of radius 6 cm and a right circular, cylinder of same radius. The, height of the cylinder so formed is, (1) 19 cm, (2) 21 cm, (3) 23 cm, (4) 25 cm, (SSC CGL Tier-I (CBE), Exam.10.09.2016), , SME–1150, , 215. If the areas of three adjacent faces of a rectangular box which, meet in a corner are 12 cm2, 15, cm 2 and 20 cm2 respectively,, then the volume of the box is, (1) 3600 cm3, (2) 300 cm3, (3) 60 cm3, (4) 180 cm3, (SSC CGL Tier-II Online, Exam.01.12.2016), , 216. A cylindrical pencil of diameter, 1.2 cm has one of its ends sharpened into a conical shape of height, 1.4 cm. The volume of the material removed is, (1) 1.056 cm3 (2) 4.224 cm3, (3) 10.56 cm3 (4) 42.24 cm3, (SSC CGL Tier-II Online, Exam.01.12.2016), , 217. A hemispherical bowl of internal, radius 9 cm, contains a liquid., This liquid is to be filled into small, cylindrical bottles of diameter 3, cm and height 4 cm. Then the, number of bottles necessary to, empty the bowl is, (1) 18, (2) 45, (3) 27, (4) 54, (SSC CGL Tier-II Online, Exam.01.12.2016), , 218. A rectangular water tank is 80, metre × 40 metre. Water flows, into it through a pipe of 40 sq.cm, at the opening at a speed of 10, km/hr. The water level will rise, in the tank in half an hour by, (1), , 3, cm., 2, , (2), , 4, cm., 9, , (3), , 5, cm., 9, , (4), , 5, cm., 8, , (SSC CGL Tier-II Online, Exam.01.12.2016)

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MENSURATION, 219. A solid cylinder has the total surface area 231 square cm. If its, curved surface area is, , 2, of the, 3, , total surface area, then the volume of the cylinder is, (1) 154 cu. cm. (2) 308 cu. cm., (3) 269.5 cu. cm (4) 370 cu. cm, , (SSC CGL Tier-II Online, Exam.01.12.2016), , 220. A right circular cylinder having, diameter 21 cm and height 38 cm, is full of ice cream. The ice cream, is to be filled in cones of height, 12 cm and diameter 7 cm having, a hemispherical shape on the top., The number of such cones to be, filled with ice cream is, (1) 54, (2) 44, (3) 36, (4) 24, (SSC CGL Tier-II Online, Exam.01.12.2016), , 221. THe sides of a rectangle with, dimension 7 cm × 11 cm are, joined to form a cylinder with, height 11 cm. What is the volume, of this cylinder?, (1) 85.75 cm3 (2) 86.92 cm3, (3) 54.25 cm3 (4) 42.875 cm3, (SSC CPO SI, ASI Online, Exam.05.06.2016) (IInd Sitting), , 222. A spherical aquarium can accommodate 11 fishes, and each fish, requires 1.54 cu. metre of water. What is the volume of the, aquarium ?, (1) 11.14 cu. metre, (2) 16.94 cu. metre, (3) 10.25 cu. metre, (4) 17.84 cu. metre, (SSC CPO Exam. 06.06.2016), (Ist Sitting), , 223. The volume of a right rectangular pyramid is 220 m3. What is, the height of the pyramid, if the, area of its base is 55 m2 ?, (1) 8 metre, (2) 13.5 metre, (3) 12 metre, (4) 9 metre, (SSC CPO Exam. 06.06.2016), (Ist Sitting), , 224. The radius of a wire is decreased, to one third. If volume remains, the same, length will increase by :, (1) 6 times, (2) 1 time, (3) 3 times, (4) 9 times, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , 225. A prism with a right triangular, base is 25 cm high. If the shorter sides of the triangle are in the, ratio of 1 : 2 and the volume of, the prism is 100 cm3, what is the, , length of the longest side of the, triangle?, (1), , 5 cm, , (3) 5 2 cm, , (2) 2 5 cm, (4) 5 cm, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , 226. The ratio of the volume of a cube, to that of a sphere which will fit, inside the cube is, (1) 4 : p, (2) 4 : 3p, (3) 6 : p, (4) 2 : p, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , 227. On a rainy day, 60 cm of rain is, recorded in a region. What is the, volume of water collected in an, open and empty rectangular water tank that measures 12 m, (length) ×10 m (width) and 50 cm, (depth)?, (1) 120 m3, (2) 72 m3, (3) 60 m3, (4) 48 m3, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , 228. How many hemispherical balls, can be made from a cylinder 56, cm high and 12 cm diameter,, when every ball being 0.75 cm, in radius?, (1) 1792, (2) 3584, (3) 4824, (4) 7168, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , 229. The number of coins of radius, 0.75 cm and thickness 0.2cm, required to be melted to make a, right circular cylinder of height 8, cm and base radius 3 cm is :, (1) 500, (2) 600, (3) 460, (4) 640, (SSC CGL Tier-I (CBE), Exam. 27.08.2016) (IInd Sitting), , 230. A sphere of radius 5 cm is melted to form a cone with base of, same radius. The height (in cm), of the cone is, (1) 5, (2) 10, (3) 20, (4) 22, (SSC CGL Tier-I (CBE), Exam. 28.08.2016) (IInd Sitting), , 231. The diameters of two cylinders, are in the ratio 3:2 and their, volumes are equal. The ratio of, their heights is, (1) 2 : 3, (2) 3 : 2, (3) 9 : 4, (4) 4 : 9, (SSC CGL Tier-I (CBE), Exam. 31.08.2016) (Ist Sitting), , SME–1151, , 232. A cylindrical container of 32 cm, height and 18 cm radius is filled, with sand. Now all this sand is, used to form a conical heap of, sand. If the height of the conical, heap is 24 cm, what is the radius of its base ?, (1) 12 cm, (2) 24 cm, (3) 36 cm, (4) 48 cm, (SSC CGL Tier-I (CBE), Exam. 31.08.2016) (Ist Sitting), , 233. A cylindrical vessel of radius 4, cm. contains water. A solid, sphere of radius 3 cm. is dipped, into the water until it is completely, immersed. The water level in the, vessel will rise by, (1) 3.5 cm., (2) 2.25 cm., (3) 2 cm., (4) 3.8 cm., (SSC CGL Tier-I (CBE), Exam. 01.09.2016) (IInd Sitting), , 234. A hollow hemispherical bowl is, made of silver with its outer radius 8 cm and inner radius 4 cm, respectively. The bowl is melted, to form a solid right circular cone, of radius 8 cm. The height of the, cone formed is, (1) 7 cm., (2) 9 cm., (3) 12 cm., (4) 14 cm., (SSC CGL Tier-I (CBE), Exam. 02.09.2016) (IInd Sitting), , 235. If the sum of radius and height, of a solid cylinder is 20 cm and, its total surface area is 880 cm.2, then its volume is, (1) 1760 cm.3 (2) 8800 cm.3, (3) 2002 cm.3 (4) 4804 cm.3, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 236. A solid sphere and a solid hemisphere have the same total surface area. The ratio of their vol-, , FG, H, , umes is Take, p =, (1) 3 3 :4, (3) 3 : 4 3, , 22, 7, , IJ, K, , (2) 4 : 3 3, (4) 1 : 12 3, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 237. The base of a right prism is a trapezium whose lengths of parallel, sides are 25 cm. and 11 cm. and, the perpendicular distance between the parallel sides is 16 cm., If the height of the prism is 10, cm., then the volume of the, prism is, (1) 1440 cu. cm., (2) 1540 cu. cm., (3) 2880 cu. cm., (4) 960 cu. cm., (SSC CGL Tier-II (CBE), Exam. 30.11.2016)

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MENSURATION, 238. The external and the internal radii of a hollow right circular cylinder of height 15 cm. are 6.75, cm. and 5.25 cm. respectively., If it is melted to form a solid cylinder of height half of the original cylinder, then the radius of, the solid cylinder is, (1) 6 cm., (2) 6.5 cm., (3) 7 cm., (4) 7.25 cm., (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 239. If a cone is divided into two parts, by drawing a plane through the, midpoints of its axis, then the, ratio of the volume of the two, parts of the cone is, (1) 1 : 2, (2) 1 : 4, (3) 1 : 7, (4) 1 : 8, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 240. A right circular cylinder is partially filled with water. Two iron, spherical balls are completely, immersed in the water so that the, height of the water in the cylinder rises by 4 cm. If the radius, of one ball is half of the other and, the diameter of the cylinder is 18, cm., then the radii of the spherical balls are, (1) 6 cm. and 12 cm., (2) 4 cm. and 8 cm., (3) 3 cm. and 6 cm., (4) 2 cm. and 4 cm., (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 244. The diagonal of a cube is, , 192, , cm. Its volume (in cm3) will be, (1) 216, (2) 432, (3) 512, (4) 624, (SSC CGL Tier-I (CBE), Exam. 02.09.2016 (IInd Sitting), , 245. The radius of the base of a right, circular cone is 6 cm and its slant, height is 10 cm. Then its volume, , FG, H, , is Use p =, (1), (2), (3), (4), , 301.71, 310.71, 301.17, 310.17, , 22, 7, , IJ, K, , cm.3, cm.3, cm.3, cm.3, , (SSC CGL Tier-I (CBE), Exam. 03.09.2016 (IIIrd Sitting), , 246. Three solid spheres have their radii r1, r2 and r3. The spheres are, melted to form a solid sphere of, bigger radius. Then the radius of, the new sphere is :, (1) (r1 + r2 + r3), (2), , e, , (3), , e, , (4), , e, , r12 + r22 + r32, r13 + r23 + r33, r14, , + r24, , j, j, , 1, 2, 1, 3, , 1, + r34 4, , j, , (SSC CGL Tier-I (CBE), Exam. 04.09.2016 (IInd Sitting), , 250. The base area of a right pyramid, is 57 sq. units and height is 10, units. Then the volume of the, pyramid is, (1) 190 cubic units, (2) 380 cubic units, (3) 540 cubic units, (4) 570 cubic units, (SSC CGL Tier-I (CBE), Exam. 09.09.2016 (IInd Sitting), , 251. The radius of a sphere and right, circular cylinder is ‘r’ units. Their, volumes are equal. The ratio of, the height and radius of the cylinder is :, (1) 3 : 1, (2) 2 : 1, (3) 3 : 2, (4) 4 : 3, (SSC CGL Tier-I (CBE), Exam. 09.09.2016 (IIIrd Sitting), , 252. The radius of cross section of a, solid right circular cylindrical rod, is 3.2 dm. The rod is melted and, 44 equal solid cubes of side 8 cm, are formed. The length of the rod, is :, , FG Take p = 22 IJ, H, 7 K, (1) 56 cm., (3) 5.6 cm., , (2) 7 cm., (4) 0.7 cm., , (SSC CGL Tier-I (CBE), Exam. 10.09.2016 (IIIrd Sitting), , 253. A cylindrical vessel of height 5, cm and radius 4 cm is completely filled with sand. When this, sand is poured out it forms a right, circular cone of radius 6 cm. What, will be the height of this cone?, , 241. The radii of two cylinders are in, the ratio of 3 : 2 and their heights, are in the ratio 3 : 7. The ratio of, their volumes is :, (1) 4 : 7, (2) 7 : 4, (3) 28 : 27, (4) 27 : 28, , 247. The ratio of the weights of two, spheres is 8 : 27 and the ratio of, weights per 1 cc of materials of, two is 8 : 1. The ratio of the radii, of the spheres is, (1) 2 : 3, (2) 1 : 3, (3) 3 : 1, (4) 3 : 2, , (SSC CGL Tier-I (CBE), Exam. 31.08.2016 (IIIrd Sitting), , (SSC CGL Tier-I (CBE), Exam. 04.09.2016 (IIIrd Sitting), , 242. If the volumes of two right circular cones are in the ratio, 1 : 4 and their diameters of bases, are in the ratio 4 : 5, then their, heights will be in the ratio :, (1) 1 : 5, (2) 4 : 25, (3) 16 : 25, (4) 25 : 64, , 248. A spherical lead ball of radius 6, cm is melted and small lead balls, of radius 3 mm are made. The, total number of possible small, lead balls is :, (1) 4250, (2) 4000, (3) 8005, (4) 8000, , 254. The radii of two cylinders are in, the ratio 2 : 3 and their heights, are in the ratio 5 : 3. The ratio of, their volumes is, (1) 27 : 20, (2) 20 : 27, (3) 4 : 9, (4) 9 : 4, , (SSC CGL Tier-I (CBE), Exam. 30.08.2016 (IIIrd Sitting), , (SSC CGL Tier-I (CBE), Exam. 07.09.2016 (IInd Sitting), , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 243. The volume of metallic cylindrical (hollow) pipe of uniform thickness is 748 c.c. Its length is 14, cm and its external radius is 9, cm. The thickness of the pipe is, (1) 0.5 cm, (2) 1.5 cm, (3) 1 cm, (4) 2 cm, (SSC CGL Tier-I (CBE), Exam. 29.08.2016 (Ist Sitting), , 249. The heights of a cone and a cylinder are equal. The radii of their, bases are in the rati o, 2 : 1. The ratio of their volumes, is :, (1) 4 : 3, (2) 3 : 4, (3) 2 : 1, (4) 1 : 2, (SSC CGL Tier-I (CBE), Exam. 07.09.2016 (IIIrd Sitting), , SME–1152, , (Take ? =, , 22, ), 7, , (1) 6.67 cm, (3) 3.33 cm, , (2) 2.22 cm, (4) 1.67 cm, , (SSC CHSL (10+2) Tier-I (CBE), Exam. 16.01.2017) (IInd Sitting), , 255. Three cubes of iron whose edges, are 6 cm, 8 cm and 10 cm respectively are melted and formed, into a single cube. The edge of, the new cube formed is, (1) 12 cm., (2) 14 cm., (3) 16 cm., (4) 18 cm., (SSC CGL Tier-II (CBE), Exam. 12.01.2017)

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MENSURATION, 256. The radius of a sphere is 6 cm., It is melted and drawn into a wire, of radius 0.2 cm. The length of, the wire is, (1) 81 metre, , (2) 80 metre, , (3) 75 metre, , (4) 72 metre, , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 257. The radius of a wire is decreased, to one-third. If volume remains, the same, length will increase by, (1) 1.5 times, , (2) 3 times, , (3) 6 times, , (4) 9 times, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 258. From each of the four corners of, a rectangular sheet of dimensions, 25 cm × 20 cm, a square of side, 2 cm is cut off and a box is made., The volume of the box is, (1) 828 cm.3, , (2) 672 cm.3, , (3) 500 cm., , (4) 1000 cm.3, , 3, , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 259. A solid sphere of radius 3 cm is, melted to form a hollow right circular cylindrical tube of length 4, cm and external radius 5 cm. The, thickness of the tube is, (1) 1 cm., , (2) 9 cm., , (3) 0.6 cm., , (4) 1.5 cm., (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 260. Three small lead spheres of radii 3 cm, 4 cm and 5 cm respectively, are melted into a single, sphere. The diameter of the new, sphere is, (1) 6 cm, , (2) 7 cm, , (3) 8 cm, , (4) 12 cm, (SSC Multi-Tasking Staff, Exam. 30.04.2017), , 261. The height of a right circular cylinder is three times the radius, of the base. If the height were, four times the radius, the volume would be 1078 cubic centimetre more than it was previously. Find the radius of the base., (1) 6 cm, , (2) 5 cm, , (3) 7.5 cm, , (4) 7 cm, , (SSC Multi-Tasking Staff, Exam. 30.04.2017), , TYPE–V, 1. A cistern 6 m long and 4 m wide,, contains water up to a depth of, 1 m 25 cm. The total area of the, wet surface is, (1) 55 m2, (2) 53.5 m2, (3) 50 m2, (4) 49 m2., (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 2. If the height of a cylinder is increased by 15 per cent and the, radius of its base is decreased, by 10 per cent then by what percent will its curved surface area, change?, (1) 3.5 per cent decrease, (2) 3.5 per cent increase, (3) 5 per cent increase, (4) 5 per cent decrease, (SSC Section Officer (Commercial Audit), , Exam. 26.11.2006 (Second, Sitting ), , 3. The radii of the base of two cylinders are in the ratio 3 : 5 and, their hei ghts in the ratio, 2 : 3. The ratio of their curved, surface will be :, (1) 2 : 5, (2) 2 : 3, (3) 3 : 5, (4) 5 : 3, (SSC CPO S.I. Exam. 16.12.2007), , 4. Water flows through a cylindrical, pipe, whose radius is 7 cm, at 5, metre per second. The time, it, takes to fill an empty water tank,, with height 1.54 metres and area, of the base (3 × 5) square metres,, is, , FG take p = 22 IJ, H, 7K, , (1) 6 minutes (2) 5 minutes, (3) 10 minutes(4) 9 minutes, (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 5. A solid cylinder has total surface, area of 462 sq.cm. Its curved, , 1, surface area is rd of the total, 3, surface area. Then the radius of, the cylinder is, (1) 7 cm, (2) 3.5 cm, (3) 9 cm, (4) 11 cm, (SSC (CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (East Zone), , 6. The diameter of a cylinder is 7, cm and its height is 16 cm. Us-, , 22, ing the value of p =, , the lat7, eral surface area of the cylinder is, , SME–1153, , (1) 352 cm.2, (3) 355 cm.2, , (2) 350 cm.2, (4) 348 cm.2, , (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (East Zone), , 7. The height of a solid right circular cylinder is 6 metres and three, times the sum of the area of its, two end faces is twice the area, of its curved surface. The radius, of its base (in metre) is, (1) 4, (2) 2, (3) 8, (4) 10, (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (East Zone), , 8. The height of a circular cylinder, is increased six times and the, base area is decreased to oneninth of its value. The factor by, which the lateral surface of the, cylinder increases is, (1) 2, (3), , 2, 3, , (2), , 1, 2, , (4), , 3, 2, , (SSC Graduate Level Tier-II, Exam.16.09.2012), , 9. The radius and height of a cylinder are in the ratio. 5 : 7 and its, volume is 550 cm3. Calculate its, curved surface area in sq. cm., (1) 110, (2) 444, (3) 220, (4) 616, (SSC CHSL DEO & LDC Exam., 28.10.2012 (Ist Sitting), , 10. The area of the curved surface, and the area of the base of a right, circular cylinder are a square cm, and b square cm respectively., The height of the cylinder is, (1), , (3), , 2a, pb, a, 2 pb, , cm, , (2), , cm (4), , a b, 2 p, a p, 2 b, , cm, , cm, , (SSC CHSL DEO & LDC Exam., 28.10.2012 (Ist Sitting), , 11. Find the length of the largest rod, that can be placed in a room 16m, long, 12m broad and 10, high., (1) 23 m., (3) 22, , 2, m., 3, , 2, m., 3, , (2) 68 m., (4) 22, , 1, m., 3, , (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting)

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MENSURATION, 12. If the volume of two cubes are in, the ratio 27 : 64, then the ratio, of their total surface area is :, (1) 27 : 64, (2) 3 : 4, (3) 9 : 16, (4) 3 : 8, (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 13. Find the length of the longest rod, that can be placed in a hall of, 10 m length, 6 m breadth and, 4 m height., (1) 2 38 m, , (2) 4 38 m, , (3) 2 19 m, , (4) 19 m, , (SSC CGL Prelim Exam. 24.02.2002, (Second Sitting), , 14. The volume of a cuboid is twice, the volume of a cube. If the dimensions of the cuboid are 9, cm, 8 cm and 6 cm, the total, surface area of the cube is :, (1) 72 cm2, (2) 216 cm2, (3) 432 cm2 (4) 108 cm2, (SSC CGL Prelim Exam. 24.02.2002, & 13.11.2005 (IInd Sitting), , 15. The length, breadth and height, of a room is 5m, 4m and 3m respectively. Find the length of the, largest bamboo that can be kept, inside the room., (1) 5 m, (2) 60 m, (3) 7 m, , (4) 5 2 m, , (SSC CGL Prelim Exam. 24.02.2002, (Middle Zone), , 16. The length of the longest rod that, can be placed in a room which is, 12 m long, 9 m broad and 8 m, high is, (1) 27 m, (2) 19 m, (3) 17 m, (4) 13 m, (SSC Section Officer (Commercial, Audit) Exam. 16.11.2003) & (SSC CPO, S.I. Exam. 06.09.2009) & (SSC CISF, Constable (GD) Exam. 05.06.2011), , 17. A cube of edge 5 cm is cut into, cubes each of edge of 1 cm. The, ratio of the total surface area of, one of the small cubes to that of, the large cube is equal to :, (1) 1 : 125, (2) 1 : 5, (3) 1 : 625, (4) 1 : 25, (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 18. The perimeter of the floor of a, room is 18 m. What is the area, of the walls of the room, if the, height of the room is 3 m ?, (1) 21 m2, (2) 42 m2, (3) 54 m2, (4) 108 m2, (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 19. The length (in metres) of the longest rod that can be put in a room, of dimensions 10 m × 10 m × 5, m is, (1) 15 3, , (2) 15, , (3) 10 2, , (4) 5 3, , (SSC CGL Tier-I Exam. 16.05.2010, (First Sitting), , 20. The floor of a room is of size 4 m, × 3 m and its height is 3 m. The, walls and ceiling of the room, require painting. The area to be, painted is, (1) 66 m2, (2) 54 m2, 2, (3) 43 m, (4) 33 m2, (SSC CGL Tier-1 Exam. 19.06.2011, (First Sitting), , 21. If the sum of three dimensions, and the total surface area of a, rectangular box are 12 cm and 94, cm 2 respectively , then the, maximum length of a stick that, can be placed inside the box is, (1) 5 2 cm, , (2) 5 cm, , (3) 6 cm, , (4) 2, , (SSC CHSL DEO & LDC Exam., 04.11.2012, Ist Sitting), , 26. Diagonal of a cube is 6 3 cm., Ratio of its total surface area and, volume (numerically) is, (1) 2 : 1, (2) 1 : 6, (3) 1 : 1, (4) 1 : 2, (SSC CHSL DEO & LDC Exam., 04.11.2012, Ist Sitting), , 27. The length of the largest possible, rod that can be placed in a cubical, room is 35 3 m. The surface, area of the largest possible sphere, that fit within the cubical room, (assuming p =, m) is, (1) 3,500, (3) 2,450, , 22. If the length of the diagonal of a, cube is 8 3 cm, then its surface, area is, (1) 192 cm2, , (2) 512 cm2, , (3) 768 cm2, , (4) 384 cm2, , FCI Assistant Grade-III, Exam. 25.02.2012 (Paper-I), North Zone (Ist Sitting), , 23. The area of the four walls of a, room is 660 m2 and its length is, twice its breadth. If the height of, the room is 11 m, then area of, its floor (in m2) is, (1) 120, (2) 150, (3) 200, (4) 330, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (North Zone), , 24. The maximum length of a pencil, that can be kept in a rectangular, box of dimensions 8cm × 6cm ×, 2cm is, (1) 2 13 cm, , (2) 2 14 cm, , (3) 2 26 cm, , (4) 10 2 cm, , (SSC CHSL DEO & LDC Exam., 28.10.2012 (Ist Sitting), , 22, ) (in square, 7, (2) 3,850, (4) 4,250, , (SSC Multi-Tasking Staff, Exam. 10.03.2013), , 5 cm, , (SSC CPO (SI, ASI & Intelligence Officer), Exam. 28.08.2011(Paper-I), , SME–1154, , 25. The volume of a cubical box is, 3.375 cubic metres. The length, of edge of the box is, (1) 75 cm, (2) 1.5 m, (3) 1.125 m, (4) 2.5 m, , 28. The volume of air in a room is, 204 m3. The height of the room, is 6 m. What is the floor area of, the room ?, (1) 32 m2, (2) 46 m2, 2, (3) 44 m, (4) 34 m2, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 29. The slant height of a conical, mountain is 2.5 km and the area, of its base is 1.54 km2. Taking, , p=, , 22, , the height of the, 7, , mountain is :, (1) 2.2 km, (3) 3 km, , (2) 2.4 km, (4) 3.11 km, , (SSC CGL Prelim Exam. 24.02.2002, (First Sitting), , 30. The base of a conical tent is 19.2, metres in di ameter and the, height of its vertex is 2.8 metres., The area of the canvas required, to put up such a tent (in square, metres) ( taki ng, nearly., (1) 3017.1, (3) 301.7, , p=, , 22, ) is, 7, , (2) 3170, (4) 30.17, , (SSC CGL Prelim Exam. 24.02.2002, & 27.07.2008 (Second Sitting)

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MENSURATION, 31. If S denotes the area of the curved, surface of a right circular cone of, height h and semivertical angle a, then S equals, (1) ph2 tan2 a, , 1, (2), ph2 tan2 a, 3, (3) ph2 sec a tan a, 1, (4), ph2 sec a tan a, 3, (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , 32. The height and the radius of the, base of a right circular cone are, 12 cm and 6cm respectively. The, radius of the circular cross-section of the cone cut by a plane, parallel to its base at a distance, of 3 cm from the base is, (1) 4 cm, (2) 5.5 cm, (3) 4.5 cm, (4) 3.5 cm, (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 33. The radius of base and slant height, of a cone are in the ratio 4 : 7. If, its curved surface area is 792 cm2,, then the radius (in cm) of its base, is [Use p = 22/7], (1) 8, (2) 12, (3) 14, (4) 16, (SSC (South Zone) Investigator, Exam. 12.09.2010), , 34. A semi-circular sheet of metal of, diameter 28 cm is bent into an, open conical cup. The depth of, the cup is approximately, (1) 11 cm, (2) 12 cm, (3) 13 cm, (4) 14 cm, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting, (East Zone), , 35. The radius and the height of a cone, are in the ratio 4 : 3. The ratio of, the curved surface area and total, surface area of the cone is, (1) 5 : 9, (2) 3 : 7, (3) 5 : 4, (4) 16 : 9, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (East Zone), , 36. A right angled sector of radius r, cm is rolled up into a cone in such, a way that the two binding radii, are joined together. Then the, curved surface area of the cone is, (1) pr2 cm2, (2) 4pr2 cm2, (3), , pr 2, cm2, 4, , (4) 2pr2 cm2, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (East Zone), , 37. The radius of the base of a coni-, , 3, sq., 7, metre canvas is required to construct the tent, then the slant, height of the tent is :, , cal tent is 16 metre. If 427, , FG Take p =, H, , 22, 7, , IJ, K, , (1) 17 metre, , (2) 15 metre, , (3) 19 metre, , (4) 8.5 metre, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (East Zone), , 38. The volume of a right circular cone, is 1232 cm 3 and its vertical, height is 24 cm. Its curved surface area is, (1) 154 cm2, (2) 550 cm2, 2, (3) 604 cm, (4) 704 cm2, (SSC CGL Prelim Exam. 11.05.2003, (Ist Sitting) & (SSC Graduate Level, , Tier-II Exam.16.09.2012, & 29.09.2013), , 39. If h, c, v are respectively the, height, curved surface area and, volume of a right circular cone,, then the value of 3pvh3 – c2h2 +, 9v2 is, (1) 2, (2) –1, (3) 1, (4) 0, (SSC Graduate Level Tier-II, Exam. 29.09.2013), , 40. If the radius of a sphere is, increased by 2 cm. its surface, area increased by 352 cm2. The, radius of sphere before change, is :, , FG use p = 22 IJ, H, 7 K, (1) 3 cm, (3) 5 cm, , (2) 4 cm, (4) 6 cm, , (SSC CGL Prelim Exam. 04.07.1999, (Ist Sitting) & (SSC CPO S.I., Exam.12.01.2003), , 41. Spheres A and B have their radii 40 cm and 10 cm respectively. Ratio of surface area of A, to the surface area of B is :, (1) 1 : 16 (2) 4 : 1, (3) 1 : 4, (4) 16 : 1, (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 42. The vol ume of a sphere i s, , a f, , 88, ´ 14, 21, , 3, , cm 3 . The curved, , surface of the sphere is (Take p, , =, , 22, ), 7, , (1) 2424 cm2, (3) 2484 cm2, , (2) 2446 cm2, (4) 2464 cm2, , (SSC CGL Prelim Exam. 11.05.2003, (Second Sitting), , 43. The surface area of a sphere is, 64pcm2. Its diameter is equal to, (1) 16 cm, (2) 8 cm, (3) 4 cm, (4) 2 cm, (SSC CPO S.I. Exam. 07.09.2003), , 44. The diameter of two hollow, spheres made from the same, metal sheet are 21 cm and 17.5, cm respectively. The ratio of the, area of metal sheets required for, making the two spheres is, (1) 6 : 5, (2) 36 : 25, (3) 3 : 2, (4) 18 : 25, (SSC CPO S.I. Exam. 05.09.2004), , 45. When the circumference of a toy, ballon is increased from 20 cm, to 25 cm, its radius (in cm) is increased by :, (1) 5, (3), , 5, 2p, , (2), , 5, p, , (4), , p, 5, , (SSC CPO S.I. Exam. 26.05.2005), , 46. If the volume and surface area of, a sphere are numerically the, same, then its radius is :, (1) 1 unit, (2) 2 units, (3) 3 units, (4) 4 units, (SSC CPO S.I. Exam. 26.05.2005), , 47. The ratio of the surface area of a, sphere and the curved surface, area of the cylinder circumscribing the sphere is, (1) 1 : 2, (2) 1 : 1, (3) 2 : 1, (4) 2 : 3, (SSC CPO S.I. Exam. 03.09.2006), , 48. The total surface area of a metallic hemisphere is 1848 cm2. The, hemisphere is melted to form a, solid right circular cone. If the, radius of the base of the cone is, the same as the radius of the, hemisphere, its height is, (1) 42 cm, (2) 26 cm, (3) 28 cm, (4) 30 cm, (SSC Section Officer (Commercial, Audit) Exam. 30.09.2007, (Second Sitting), , 49. If the radii of two spheres are in, the ratio 1 : 4, then their surface, area are in the ratio :, (1) 1 : 2, (2) 1 : 4, (3) 1 : 8, (4) 1 : 16, (SSC CPO S.I. Exam. 16.12.2007), , SME–1155

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MENSURATION, 50. A solid metallic sphere of radius, 8 cm is melted to form 64 equal, small solid spheres. The ratio of, the surface area of this sphere, to that of a small sphere is, (1) 4 : 1, (2) 1 : 16, (3) 16 : 1, (4) 1 : 4, (SSC CGL Prelim Exam. 27.07.2008, (First Sitting), , 51. If S1 and S2 be the surface area, of a sphere and the curved surface area of the circumscribed, cylinder respectively, then S1 is, equal to, (1), , 3, S, 4 2, , (2), , 1, S, 2 2, , (3), , 2, S, 3 2, , (4) S2, , 52. The volume of two spheres are, in the ratio 8 : 27. The ratio of, their surface area is :, (1) 4 : 9, (2) 2 : 3, (3) 4 : 5, (4) 5 : 6, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 53. The volume of a solid hemisphere, is 19404 cm3. Its total surface, area is, (1) 4158 cm2 (2) 2858 cm2, (3) 1738 cm2 (4) 2038 cm2, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 54. A sphere and a hemisphere have, the same volume. The ratio of, their curved surface area is :, (1) 2, , -, , 3, 2, , :1, , 2, , (3) 4 3 : 1, , (2), , (1) 9 3 cm, , (2) 3 cm, , (3) 3 3 cm, , (4) 9 cm, , (SSC Graduate Level Tier-I, Exam. 19.05.2013 Ist Sitting), , 58. The base of a solid right prism is a, triangle whose sides are 9 cm, 12, cm and 15 cm. The height of the, prism is 5 cm. Then, the total surface area of the prism is, (1) 180 cm2, (2) 234 cm2, (3) 288 cm2, (4) 270 cm2, (SSC CPO (SI, ASI & Intelligence Officer), Exam. 28.08.2011 (Paper-I), , (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , -, , 57. If the total surface area of a hemisphere is 27p square cm, then, the radius of the base of the hemisphere is, , 2, 23, , :1, , 1, , (4) 2 3 : 1, , (SSC CHSL DEO & LDC, Exam. 21.10.2012 (IInd Sitting), , 55. If the radius of a sphere be doubled, the area of its surface will, become, (1) Double, (2) Three times, (3) Four times, (4) None of the mentioned, (SSC CHSL DEO & LDC, Exam. 28.10.2012 (Ist Sitting), , 56. A solid hemisphere is of radius, 11 cm. The curved surface area, in sq. cm is, (1) 1140.85, (2) 1386.00, (3) 760.57, (4) 860.57, (SSC Graduate Level Tier-I, Exam. 11.11.2012 (Ist Sitting), , 59. The base of a right prism is an, equilateral triangle of area 173, cm2 and the volume of the prism, is 10380 cm3. The area of the, lateral surface of the prism is (use, , 3 = 1.73), (1) 1200 cm2, (3) 3600 cm2, , (2) 2400 cm2, (4) 4380 cm2, , (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (East Zone), , 60. The base of a right pyramid is a, square of side 16 cm long. If its, height be 15 cm, then the area, of the lateral surface in square, centimetre is :, (1) 136, (2) 544, (3) 800, , (4) 1280, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (East Zone), , 61. If the slant height of a right pyramid with square base is 4 metre and the total slant surface of, the pyramid is 12 square metre,, then the ratio of total slant surface and area of the base is :, (1) 16 : 3, (2) 24 : 5, (3) 32 : 9, (4) 12 : 3, (SSC CHSL DEO & LDC, Exam. 21.10.2012 (IInd Sitting), , 62. The base of a right pyramid is an, equilateral triangle of side 10 3, cm. If the total surface area of, , 63. A right prism stands on a base 6, cm equilateral triangle and its volume is 81 3 cm3 . The height (in, cm) of the prism is, (1) 9, (2) 10, (3) 12, (4) 15, (SSC CHSL DEO & LDC Exam., 27.10.2013 IInd Sitting), , 64. A right pyramid stands on a, square base of diagonal 10 2, cm. If the height of the pyramid, is 12 cm, the area (in cm2) of its, slant surface is, (1) 520, (2) 420, (3) 360, (4) 260, (SSC CHSL DEO & LDC, Exam. 10.11.2013, Ist Sitting), , 65. If the altitude of a right prism is, 10 cm and its base is an equilateral triangle of side 12 cm, then, its total surface area (in cm2) is, (1) (5 + 3 3 ) (2) 36 3, (3) 360, , (4) 72(5+ 3 ), , (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 66. A right pyramid stands on a base, 16 cm square and its height is, 15 cm. The area (in cm2) of its, slant surface is, (1) 514, (2) 544, (3) 344, (4) 444, (SSC CHSL DEO & LDC Exam., 10.11.2013, IInd Sitting), , 67. The base of a right prism is a rightangled triangle whose sides are, 5 cm, 12 cm and 13 cm. If the, area of the total surface of the, prism is 360 cm2, then its height, (in cm) is, (1) 10, (2) 12, (3) 9, (4) 11, (SSC CHSL DEO & LDC Exam., 10.11.2013, IInd Sitting), , 68. A hemisphere and a cone have, equal base. If their heights are, also equal, the ratio of their, curved surface will be :, , the pyramid is 270 3 sq. cm,, its height is, , (1) 1 : 2, , (2), , (3) 1 : 2, , (4) 2 : 1, , (1) 12 3 cm, , (2) 10 cm, , (SSC CGL Prelim Exam. 24.02.2002, , (3) 10 3 cm, , (4) 12 cm, , (SSC CHSL DEO & LDC, Exam. 20.10.2013), , SME–1156, , 2 :1, , & 13.11.2005 (Ist Sitting) &, (SSC CGL Tier-I Exam. 26.06.2011, (IInd Sitting) & (SSC CHSL DEO, & LDC Exam. 11.12.2011, (Ist Sitting) (Delhi Zone)

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MENSURATION, 69. A right circular cylinder just encloses a sphere of radius r. The, ratio of the surface area of the, sphere and the curved surface, area of the cylinder is, (1) 2 : 1, (2) 1 : 2, (3) 1 : 3, (4) 1 : 1, (SSC SAS Exam. 26.06.2010, (Paper-1), , 70. A sphere and a cylinder have, equal volume and equal radius., The ratio of the curved surface, area of the cylinder to that of the, sphere is, (1) 4 : 3, (2) 2 : 3, (3) 3 : 2, , (4) 3 : 4, , (SSC Multi-Tasking (Non-Technical), Staff Exam. 27.02.2011) & (SSC, CHSL DEO & LDC Exam. 04.11.2012, (IInd Sitting), , 71. A circus tent is cylindrical up to, a height of 3 m and conical above, it. If its diameter is 105m and, the slant height of the conical part, is 63 m, then the total area of, the canvas required to make the, , e, , 22, tent is take p = 7, , j, , (1) 11385 m2, , (2) 10395 m2, , (3) 9900 m2, , (4) 990 m2, , (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (Delhi Zone), , 72. A right circular cylinder and a, cone have equal base radius and, equal height. If their curved surfaces are in the ratio 8 : 5, then, the radius of the base to the, height are in the ratio :, (1) 2 : 3, (2) 4 : 3, (3) 3 : 4, (4) 3 : 2, (SSC CHSL DEO & LDC Exam., 11.12.2011 (IInd Sitting (Delhi Zone), , 73. The base of a cone and a cylinder have the same radius 6 cm., They have also the same height, 8 cm. The ratio of the curved, surface of the cylinder to that of, the cone is, (1) 8 : 5, (2) 8 : 3, (3) 4 : 3, (4) 5 : 3, (SSC CHSL DEO & LDC Exam., 21.10.2012 (Ist Sitting), , 75. A square of side 3 cm is cut off, from each corner of a rectangular, sheet of length 24 cm and breadth, 18 cm and the remaining sheet, is folded to form an open, rectangular box. The surface area, of the box is, (1) 468 cm2, (2) 396 cm2, (3) 612 cm2, (4) 423 cm2, (SSC CHSL DEO & LDC, Exam. 20.10.2013), , 76. Three solid iron cubes of edges, 4 cm, 5 cm and 6 cm are melted, together to make a new cube. 62, cm3 of the melted material is lost, due to improper handling. The, area (in cm2) of the whole surface of the newly formed cube is, (1) 294, (2) 343, (3) 125, (4) 216, (SSC CHSL DEO & LDC Exam., 10.11.2013, IInd Sitting), , 77. If each edge of a cube is increased by 50%, the percentage, increase in its surface area is, (1) 150%, (2) 75%, (3) 100%, (4) 125%, (SSC FCI Assistant Grade-III Main, , Exam. 07.04.2013) & (SSC GL, Tier-II Exam. 29.09.2013), , 78. The length of each edge of a regular tetrahedron is 12 cm. The, area (in sq. cm) of the total surface of the tetrahedron is, (1) 288 3, , (2) 144 2, , (3) 108 3, , (4) 144 3, , (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , 79. A toy is in the form of a cone, mounted on a hemisphere. The, radius of the hemisphere and that, of the cone is 3 cm and height of, the cone is 4 cm. The total surface area of the toy (taking p =, , 22, ) is, 7, (1), (2), (3), (4), , 75.43 sq. cm., 103.71 sq. cm., 85.35 sq. cm., 120.71 sq. cm., , (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (North Zone), , 74. A solid right circular cylinder and, a solid hemisphere stand on equal, bases and have the same height., The ratio of their whole surface, area is:, (1) 3 : 2, (2) 3 : 4, (3) 4 : 3, (4) 2 : 3, , 80. Area of the floor of a cubical room, is 48 sq.m. The length of the, longest rod that can be kept in, that room is, (1) 9 metre, (2) 12 metre, (3) 18 metre, (4) 6 metre, , (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , SME–1157, , 81. A sphere and a hemisphere have, the same radius. Then the ratio, of their respective total surface, areas is, (1) 2 : 1, (2) 1 : 2, (3) 4 : 3, (4) 3 : 4, (SSC CGL Tier-I, Re-Exam. (2013) 27.04.2014), , 82. If the surface area of a sphere is, 346.5 cm 2 , then its radius, , LMtaking p = 22 OP, 7 Q, N, , is, , (1) 7 cm, , (2) 3.25 cm, , (3) 5.25 cm, , (4) 9 cm, , (SSC CGL Tier-II Exam. 21.09.2014), , 83. The base of a prism is a right angled triangle with two sides 5 cm, and 12 cm. The height of the, prism is 10 cm. The total surface area of the prism is, (1) 360 sq cm (2) 300 sq cm, (3) 330 sq cm (4) 325 sq cm, (SSC CGL Tier-II Exam. 21.09.2014), , 84. The ratio of the length and, breadth of a rectangular parallelopiped is 5 : 3 and its height is, 6 cm. If the total surface area of, the parallelopiped be 558 sq. cm,, then its length in dm is, (1) 9, (2) 1.5, (3) 10, (4) 15, (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014), , 85. Deepali makes a model of a cylindrical kaleidoscope for her science project. She uses a chart, paper to make it. If the length of, the kaleidoscope is 25 cm and, radius 3-5 cm, the area of the, paper she used, in square cm, is, , FG p = 22 IJ, H 7K, (1) 1100, (3) 500, , (2) 550, (4) 450, , (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014), , 86. If the sum of the dimensions of a, rectangular parallelopiped is 24, cm and the length of the diagonal is 15 cm, then the total surface area of it is, (1) 420 cm2, (2) 275 cm2, 2, (3) 351 cm, (4) 378 cm2, (SSC CHSL DEO & LDC, Exam. 9.11.2014)

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MENSURATION, 87. The length, breadth and height, of a cuboid are in the ratio, 3 : 4 : 6 and its volume is 576, cm 3. The whole surface of the, cuboid is, (1) 216 cm2, (2) 324 cm2, 2, (3) 432 cm, (4) 460 cm2, (SSC CHSL DEO Exam. 02.11.2014, (Ist Sitting), , 88. The radius of a right circular cone, is 3 cm and its height is 4 cm., The total surface area of the, cone is, (1) 48.4 sq.cm (2) 64.4 sq.cm, (3) 96.4 sq.cm (4) 75.4 sq.cm, (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam. 22.06.2014, TF No. 999 KP0), , 89. There are two cones. The curved, surface area of one is twice that, of the other. The slant height of, the latter is twice that of the, former. The ratio of their radii is, (1) 4 : 1, (2) 4 : 3, (3) 3 : 4, (4) 1 : 4, (SSC CGL Tier-I Exam. 19.10.2014, TF No. 022 MH 3), , 90. From a solid right circular cylinder of length 4 cm and diameter, 6 cm, a conical cavity of the same, height and base is hollowed out., The whole surface of the remaining solid (in square cm.) is, (1) 48 p, (2) 15 p, (3) 63 p, , (4) 24 p, , (SSC CGL Tier-II Exam. 12.04.2015, TF No. 567 TL 9), , 91. The length, breadth and height, of a wooden box with a lid are 10, cm, 9 cm and 7 cm, respectively. The total inner surface of the, closed box is 262 cm2. The thickness of the wood (in cm.) is, (1) 2, (2) 3, (3), , 23, 3, , (4) 1, , (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 92. The total surface area of a regular triangular pyramid with each, edge of length 1 cm is, (1) 4 3, (3), , cm2, , 3 cm2, , 4, 3 cm2, (2), 3, (4) 4 cm2, , (SSC CAPFs SI, CISF ASI & Delhi, , Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 93. The number of paving stones, each measuring 2.5m × 2m required to pave a rectangular, courtyard 30m long and 17.5 m, wide, is, (1) 80, (2) 33, (3) 99, (4) 105, (SSC CAPFs SI, CISF ASI & Delhi, Police SI Exam, 21.06.2015, (Ist Sitting) TF No. 8037731), , 94. The length of canvas, 75 cm wide, required to build a conical tent of, height 14m and the floor area, 346.5 m2 is, (1) 665 m, (3) 490 m, , (2) 860 m, (4) 770 m, , (SSC CGL Tier-I Exam, 09.08.2015, (IInd Sitting) TF No. 4239378), , 95. 5 persons will live in a tent. If, each person requires 16m 2 of, floor area and 100m3 space for, air then the height of the cone of, smallest size to accommodate, these persons would be, (1) 16 metre (2) 10.25 metre, (3) 20 metre (4) 18.75 metre, (SSC CGL Tier-I Exam, 16.08.2015, (Ist Sitting) TF No. 3196279), , 96. The paint in a certain container, is sufficient to paint an area equal, to 9.375 m2. How many bricks, measuring 22.5 cm by 10 cm by, 7.5 cm can be painted out of this, container?, (1) 200, (2) 1000, (3) 10, (4) 100, (SSC CGL Tier-I, Re-Exam, 30.08.2015), , 97. The ratio between the length and, the breadth of a rectangular park, is 3 : 2. If a man cycling along, the boundary of the park at the, speed of 12 kmph completes one, round in 8 minutes, then the area, of the park is equal to, (1) 152600 m2 (2) 153500 m2, (3) 153600 m2 (4) 153800 m2, (SSC CGL Tier-I, Re-Exam, 30.08.2015), , 98. The base of a right pyramid is a, square of side 10 cm. If the height, of the pyramid is 12 cm, then its, total surface area is, (1) 400 cm2 (2) 460 cm2, (3) 260 cm2 (4) 360 cm2, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , SME–1158, , 99. There is a wooden sphere of radius 6 3 cm. The surface area, of the largest possible cube cut, out from the sphere will be, (1) 864 cm2 (2) 464 3 cm2, (3) 462 cm2 (4) 646 3 cm2, (SSC CGL Tier-II Exam,, 25.10.2015, TF No. 1099685), , 100. A hemisphere and a cone have, equal bases. If their heights are, also equal, then the ratio of their, curved surfaces will be, (1) 1 : 2, (2) 2 : 1, (3) 1 :, , 2, , (4), , 2 :1, , (SSC CHSL (10+2) LDC, DEO & PA/SA, Exam, 01.11.2015, IInd Sitting), , 101. The radius of base and curved, surface area of a right cylinder is, ‘r’ units and 4prh square units, respectively. The height of the, cylinder is :, (1), , h, units, 2, , (3) 2h units, , (2) h units, (4) 4h units, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (Ist Sitting) TF No. 6636838), , 102. A hemispherical bowl has 3.5 cm, radius. It is to be painted inside, as well as outside. The cost of, painting it at the rate of Rs. 5, per 10 sq. cm will be:, (1) Rs. 77, (2) Rs. 100, (3) Rs. 175, (4) Rs. 50, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (Ist Sitting) TF No. 6636838), , 103. The total surface area of a right, circular cylinder with radius of, the base 7 cm and height 20, cm, is:, (1) 900 cm2, (2) 140 cm2, 2, (3) 1000 cm, (4) 1188 cm2, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 15.11.2015, (Ist Sitting) TF No. 6636838), , 104. If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm2., The radius of the sphere initially, was :, , FG use p = 22 IJ, H, 7 K, , (1) 4 cm, (3) 3 cm, , (2) 5 cm, (4) 6 cm, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (Ist Sitting) TF No. 1375232)

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MENSURATION, 105. The diameter of a 120 cm long, roller is 84 cm. It takes 500 complete revolutions of the roller to, level a ground. The cost of levelling the ground at Rs. 1.50 per, sq. m. is :, (1) Rs. 6000 (2) Rs. 3762, (3) Rs. 2376 (4) Rs. 5750, (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (Ist Sitting) TF No. 1375232), , 106. A hemispherical bowl has internal radius of 6 cm. The internal, surface area would be : (Take p ¾, 3-14), (1) 225 cm2, (2) 400 cm2, (3) 289-75 cm2 (4) 226-08 cm2, , 111. The area of the largest sphere (in, cm2) that can be drawn inside a, square of side 18 cm is, (1) 972p, (2) 1166p, (3) 36p, , 112. The total surface area of a right, pyramid on a square base of side, 10 cm with height 12 cm is :, (1) 260 square cm, (2) 360 square cm, (3) 330 square cm, (4) 300 square cm, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , (SSC CHSL (10+2) LDC, DEO, , & PA/SA Exam, 06.12.2015, (IInd Sitting) TF No. 3441135), , 107. The surface area of a sphere is, 616 cm 2. The volume of the, sphere would be :, (1) 1437, , 1, cm2 (2) 2100 cm2, 3, , (3) 2500 cm2, , 3, cm2, (4) 1225, 5, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, , (IInd Sitting) TF No. 3441135), , 108. Thousand solid metallic spheres, of diameter 6 cm each are melted and recast into a new solid, sphere. The diameter of the new, sphere (in cm) is, (1) 30, (2) 90, (3) 45, (4) 60, , 113. The base of a right prism, whose, height is 2 cm, is a square. If the, total surface area of the prism is, 10 cm2, then its volume is :, (1) 3 cm3, (2) 1 cm3, 3, (3) 2 cm, (4) 4 cm3, (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , 114. Let ABCDEF be a prism whose, base is a right angled triangle,, where sides adjacent to 90° are, 9 cm and 12 cm. If the cost of, painting the prism is Rs. 151.20,, at the rate of 20 paise per sq cm, then the height of the prism is :, (1) 17 cm, , (2) 18 cm, , (3) 15 cm, , (4) 16 cm, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 20.03.2016), (IInd Sitting), , (SSC CGL Tier-I (CBE), Exam.11.09.2016) (Ist Sitting), , 109. The lateral surface area of frustum of a right circular cone, if, the area of its base is 16p cm2, and the diameter of circular upper surface is 4 cm and slant, height is 6 cm, will be, (1) 30p cm2, (2) 48p cm2, (3) 36p cm2, (4) 60p cm2, (SSC CGL Tier-II Online, Exam.01.12.2016), , (4) 288p, , (SSC CHSL (10+2) Tier-I (CBE), Exam. 08.09.2016) (Ist Sitting), , 115. A right circular cylindrical tunnel, of diameter 5m and length 10m, is to be constructed from a sheet, of iron. The area of iron sheet, required will be :, (1) 52p, (2) 50p, (3) 51p, , (4) 49p, , (SSC CPO SI & ASI, Online, Exam. 06.06.2016) (IInd Sitting), , 110. The diameter of a sphere is twice, the diameter of another sphere., The surface area of the first, sphere is equal to the volume of, the second sphere. The magnitude of the radius of the first, sphere is, (1) 12, (2) 24, (3) 16, (4) 48, , 116. If h, C, V are respectively the, height, the curved surface and, , (SSC CGL Tier-II Online, Exam.01.12.2016), , (SSC CPO SI & ASI, Online, Exam. 06.06.2016) (IInd Sitting), , the volume of a cone, then, 3pVh3 – C2h2 + 9V2 = ?, (1) 0, (3), , 1, 2, , 117. The length of the two parallel, sides of a trapezium are 16m and, 20m respectively. If its height is, 10m, its area in square metre is, (1) 360, (2) 260, (3) 240, (4) 180, (SSC CGL Tier-I (CBE), Exam. 27.08.2016) (Ist Sitting), , 118. Three medians AD, BE and CF of, DABC intersect at G. The area of, D ABC is 36 sq. cm. Then the area, of D CGE is, (1) 12 sq. cm. (2) 6 sq. cm., (3) 9 sq. cm. (4) 18 sq. cm., (SSC CGL Tier-I (CBE), Exam. 27.08.2016) (Ist Sitting), , 119. The diagonal of a cuboid of length, 5 cm, width 4 cm and height 3, cm is, (1) 5 2 cm., , (2) 2 5 cm., , (3) 12 cm., , (4) 10 cm., , (SSC CGL Tier-I (CBE), Exam. 30.08.2016) (Ist Sitting), , 120. A well of diameter 3m is dug 14m, deep. The earth taken out of it, has been spread evenly all around, it in the shape of a circular ring, of width 4m to form an embankment. Find the height of the embankment., (1) 4.25m, (2) 2.25m, (3) 1.125m, (4) 1.75m, (SSC CGL Tier-I (CBE), Exam. 02.09.2016) (IInd Sitting), , 121. The diameter of a sphere is twice, the diameter of another sphere., The curved surface area of the first, and the volume of the second are, numerically equal. The numerical, value of the radius of the first, sphere is, (1) 3, (2) 24, (3) 8, (4) 16, (SSC CGL Tier-I (CBE), Exam. 03.09.2016) (IInd Sitting), , 122. A sphere has the same curved, surface area as a cone of vertical, height 40 cm and radius 30 cm., The radius of the sphere is, , (2) 3, , (1) 5 5 cm, , (2) 5 3 cm, , (4) 11, , (3) 5 15 cm, , (4) 5 10 cm, , SME–1159, , (SSC CGL Tier-I (CBE), Exam. 04.09.2016) (Ist Sitting)

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MENSURATION, 123. The whole surface area of a pyramid whose base is a regular, polygon is 340 cm.2 and area of, its base is 100 cm2. Area of each, lateral face is 30 cm2. Then the, number of lateral faces is, (1) 8, (2) 9, (3) 7, (4) 10, (SSC CGL Tier-II (CBE), Exam. 30.11.2016), , 124. A right circular conical structure, stands on a circular base of 21, metre diameter and is 14 metre, in height. The total cost of colour, washing for its curved surface at, Rs. 6 per square metre is, , FG Take p =, H, , 22, 7, , (1) Rs. 4365, (3) Rs. 3465, , IJ, K, , (2) Rs. 4465, (4) Rs. 3365, , (SSC CGL Tier-I (CBE), Exam. 10.09.2016 (IInd Sitting), , 125. If curved surface area of a cylinder is 1386 sq cm and height is, 21 cm, what will be its radius?, , FG Take p = 22 IJ, H, 7 K, , (1) 21 cm., (3) 10.5 cm., , (2) 5.25 cm., (4) 15.75 cm., , (SSC CHSL (10+2) Tier-I (CBE), Exam. 15.01.2017) (IInd Sitting), , 126. The height and the total surface, area of a right circular cylinder, are 4 cm and 8p sq.cm. respectively. The radius of the base of, cylinder is, (1), (2), , e2 2 – 2j cm., e2 – 2 j cm., , (3) 2 cm., (4), 2 cm., , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 22, 5 = 2.23 and p =, 7, , (1) 1.42 litres (2) 1.53 litres, (3) 1.71 litres (4) 1.82 litres, , 1. The circumference of the base of, a circular cylinder is 6p cm. The, height of the cylinder is equal to, the diameter of the base. How, many litres of water can it hold?, (1) 54 p cc, (2) 36 p cc, (3) 0.054 p cc (4) 0.54 p cc, (SSC CGL Prelim Exam. 27.02.2000, (First Sitting), , 2. The diameter of the base of a cylindrical drum is 35 dm. and the, height is 24 dm. It is full of, kerosene. How many tins each, of size 25 cm × 22 cm × 35 cm, can be filled with kerosene from, the drum?, , 22, (Use p =, ), 7, (1) 1200, (3) 600, , (2) 1020, (4) 120, , (SSC CPO S.I. Exam. 07.09.2003), , 3. Marbles of diameter 1.4 cm are, dropped into a cylindrical beaker containing some water and, are fully submerged. The dia, meter of the beaker is 7 cm. Find, how many marbles have been, dropped in it if the water rises, by 5.6 cm ?, (1) 50, (2) 150, (3) 250, (4) 350, (SSC CGL Tier-1 Exam. 26.06.2011, (Second Sitting), , 4. A right cylindrical vessel is full, with water. How many right, cones having the same diameter, and height as that of the right, cylinder will be needed to store, , 127. The radius of a cylindrical milk, container is half its height and, surface area of the inner part is, 616 sq. cm. The amount of milk, that the container can hold, approximately, is, , LMUse :, N, , TYPE–VI, , OP, Q, , (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , 128. A solid brass sphere of radius 2.1, dm is converted into a right circular cylindrical rod of length 7, cm. The ratio of total surface areas of the rod to the sphere is, (1) 3 : 1, (2) 1 : 3, (3) 7 : 3, (4) 3 : 7, (SSC CGL Tier-II (CBE), Exam. 12.01.2017), , that water ? (Take p =, (1) 4, (3) 3, , 22, )., 7, , (2) 2, (4) 5, (SSC Delhi Police S.I. (SI), Exam. 19.08.2012), , 5. How many cubes, each of edge 3, cm, can be cut from a cube of, edge 15 cm?, (1) 25, (2) 27, (3) 125, (4) 144, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 6. A cuboidal block of 6 cm × 9 cm, × 12 cm is cut up into exact number of equal cubes. The least possible number of cubes will be, (1) 6, (2) 9, (3) 24, (4) 30, (SSC Section Officer (Commercial, Audit) Exam. 16.11.2003), , SME–1160, , 7. A soap cake is of size 8 cm × 5, cm × 4 cm. The number of such, soap cakes that can be packed, in a box measuring 56 cm × 35, cm × 28 cm is :, (1) 49, (2) 196, (3) 243, (4) 343, (SSC CGL Prelim Exam. 08.02.2004, (Second Sitting), , 8. The cost of carpeting a room is, 120. If the width had been 4, metres less, the cost of the Carpet would have been 20 less., The width of the room is :, (1) 24 m, (2) 20 m, (3) 25 m, (4) 18.5 m, (SSC CPO S.I. Exam. 26.05.2005), , 9. A hall 25 metres long and 15, metres broad is surrounded by a, verandah of uniform width of 3.5, metres. The cost of flooring the, verandah, at 27.50 per square, metre is, (1), , 9149.50, , (2), , 8146.50, , (3), , 9047.50, , (4), , 4186.50, , (SSC Graduate Level Tier-I, Exam. 11.11.2012 (Ist Sitting), , 10. A cube of edge 6 cm is painted, on all sides and then cut into unit, cubes. The number of unit cubes, with no sides painted is, (1) 0, (2) 64, (3) 186, (4) 108, (SSC Delhi Police S.I. (SI), Exam. 19.08.2012), , 11. The height of a conical tank is 60, cm and the diameter of its base, is 64cm. The cost of painting it, from outside at the rate of 35, per sq. m. is :, (1) 52.00 approx., (2) 39.20 approx., (3) 35.20 approx., (4) 23.94 approx., (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting), , 12. Some solid metallic right circular cones, each with radius of, the base 3 cm and height 4 cm,, are melted to form a solid sphere, of radius 6 cm. The number of, right circular cones is, (1) 12, (2) 24, (3) 48, (4) 6, (SSC CPO S.I. Exam. 03.09.2006)

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MENSURATION, 13. The diameter of a circular wheel, is 7 m. How many revolutions, will, it make in travelling 22, km ?, (1) 100, (2) 400, (3) 500, (4) 1000, (SSC Graduate Level Tier-II, , Exam. 29.09.2013), , 14. A spherical lead ball of radius, 10cm is melted and small lead, balls of radius 5mm are made., The total number of possible, small lead balls is (Take p =, , 22, ), 7, (1) 8000, (3) 800, , (2) 400, (4) 125, (SSC Delhi Police S.I. (SI), Exam. 19.08.2012), , 15. The total number of spherical, bullets, each of diameter 5 decimeter, that can be made by utilizing the maximum of a rectangular block of lead with 11 metre, length, 10 metre breadth and, 5 metre width is (assume that, p > 3), (1) equal to 8800, (2) less than 8800, (3) equal to 8400, (4) greater than 9000, (SSC Graduate Level Tier-II, , Exam. 29.09.2013), , 16. A solid metallic cone of height 10, cm, radius of base 20 cm is, melted to make spherical balls, each of 4 cm diameter. How, many such balls can be made ?, (1) 25, (2) 75, (3) 50, (4) 125, (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting), , 17. A cylindrical rod of iron whose, height is eight times its radius is, melted and cast into spherical, balls each of half the radius of, the cylinder. The number of, such spherical balls is, (1) 12, (2) 16, (3) 24, (4) 48, (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (North Zone), , 18. The number of spherical bullets, that can be made out of a solid, cube of lead whose edge measures 44 cm, each bullet being, of 4 cm diameter, is (take p =, 22 ), 7, (1) 2541, (2) 2451, (3) 2514, (4) 2415, (SSC Constable (GD) & Rifleman, (GD) Exam. 22.04.2012 (Ist Sitting), , 19. The radius of a metallic cylinder, is 3 cm and its height is 5 cm., It is melted and moulded into, small cones, each of height 1, cm and base radius 1 mm. The, number of such cones formed, is, (1) 450, (2) 1350, (3) 8500, (4) 13500, (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , 20. If a metallic cone of radius 30 cm, and height 45 cm is melted and, recast into metallic spheres of, radius 5 cm, find the number of, spheres., (1) 81, (2) 41, (3) 80, (4) 40, (SSC Graduate Level Tier-I, Exam. 21.04.2013 IInd Sitting), , 21. Water flows at the rate of 10, metres per minute from a cylindrical pipe 5 mm in diameter., How long it take to fill up a conical vessel whose diameter at the, base is 30 cm and depth 24, cm ?, (1) 28 minutes 48 seconds, (2) 51 minutes 12 seconds, (3) 51 minutes 24 seconds, (4) 28 minutes 36 seconds, (SSC CAPFs SI & CISF ASI, Exam. 23.06.2013), , 22. A metallic sphere of radius 10.5, cm is melted and then recast, into small cones each of radius, 3.5 cm and height 3 cm. The, number of cones thus formed is, (1) 140, (2) 132, (3) 112, (4) 126, (SSC CHSL DEO & LDC Exam., 10.11.2013, Ist Sitting), , 23. The radius of the base of a Conical tent is 12 m. The tent is 9, m high. Find the cost of canvas, required to make the tent, if one, square metre of canvas costs, 120, (Take p = 3.14 ), (1), 67, 830, (2), 67, 800, (3), 67, 820, (4), 67, 824, (SSC CGL Tier-I Re-Exam. (2013), 20.07.2014 (Ist Sitting), , 24. If the radius of a cylinder is decreased by 50 % and the height, is increased by 50 %, then the, change in volume is, (1) 52.5 %, (2) 67.5 %, (3) 57.5 %, (4) 62.5 %, (SSC CHSL DEO & LDC, Exam. 02.11.2014 (IInd Sitting), , SME–1161, , 25. The base of a triangle is increased by 10%. To keep the, area unchanged the height of the, triangle is to be decreased by, (1) 9, , 1, %, 11, , (3) 11%, , (2) 11, , 1, %, 9, , (4) 9%, , (SSC CHSL (10+2) DEO & LDC, Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , 26. If the area of the base of a cone, is increased by 100%, then the, volume increases by, (1) 200%, (2)182%, (3) 141%, (4) 100%, (SSC CGL Tier-II Exam,, 2014 12.04.2015 (Kolkata Region), TF No. 789 TH 7), , 27. The percentage increase in the, surface area of a cube when, each side is doubled is, (1) 50%, (2) 200%, (3) 150%, (4) 300%, (SSC CGL Tier-I Exam, 09.08.2015, (IInd Sitting) TF No. 4239378), , 28. Each side of a cube is decreased, by 25%. Find the ratio of the volumes of the original cube and the, resulting cube., (1) 8 : 1, (2) 27 : 64, (3) 64 : 1, (4) 64 : 27, (SSC CHSL (10+2) LDC, DEO & PA/SA, Exam, 01.11.2015, IInd Sitting), , 29. If water is freezed to become ice,, its volume is increased by 10%,, then if the ice is melted to water again, its volume will be decreased by :, (1) 9%, , (2) 9, , 1, %, 11, , (3) 8%, , (4) 9, , 1, %, 2, , (SSC CHSL (10+2) LDC, DEO, & PA/SA Exam, 06.12.2015, (IInd Sitting) TF No. 3441135), , 30. If the radius of a right circular, cylinder open at both the ends,, is decreased by 25% and the, height of the cylinder is increased, by 25%. Then the curved surface area of the cylinder thus, formed, (1) remains unaltered, (2) is increased by 25%, (3) is increased by 6.25%, (4) is decreased by 6.25%, (SSC CGL Tier-II Online, Exam.01.12.2016)

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MENSURATION, 31. The amount of concrete required, to build a concrete cylindrical pillar whose base has a perimeter, 8.8 metre and curved surface area, 17.6 square metre, is, , FG Take p = 22 IJ, H, 7 K, , (1) 8.325 m3, (3) 10.5 m3, , 36. An inverted conical shaped vessel is filled with water to its brim., The height of the vessel is 8 cm, and radius of the open end is 5, cm. When a few solid spherical, metallic balls each of radius, , (2) 9.725 m3, (4) 12.32 m3, , (SSC CGL Tier-II Online, Exam.01.12.2016), , 32. A big cube is formed by arranging the 160 coloured and 56 noncoloured similar cubes in such a, way that the exposure of the coloured cubes to the outside is, minimum. The percentage of exposed area that is coloured is, (1) 25.9%, (2) 44.44%, (3) 35%, (4) 46%, (SSC CPO Exam. 06.06.2016), (Ist Sitting), , 33. If the radius of the base, and the, height of a right circular cone are, increased by 20%, what is the, approximate percentage increase, in volume ?, (1) 60, (2) 68.8, (3) 72.8, (4) 75, (SSC CPO Exam. 06.06.2016), (Ist Sitting), , 34. Which of the the following statements is not correct?, (1) For a given radius and height,, a right circular cone has the, lesser volume among a right circular cone and a right circular, cylinder., (2) If side of a cube is increased, by 10%, the volume will increase by 33.1%., (3) If the radius of a sphere is increased by 20%, the surface, area will increase by 40%., (4) Cutting a sphere into 2 parts, does not change the total volume., , cm are dropped in the vessel,, 25% water is overflowed. The, number of balls is :, (1) 100, (2) 400, (3) 200, (4) 150, (SSC CGL Tier-I (CBE), Exam. 11.09.2016 (IInd Sitting), , 37. The radius and the height of a, cone are each increased by 20%., Then the volume of the cone increases by, (1) 20%, (2) 20.5%, (3) 62%, (4) 72.8%, (SSC CGL Tier-I (CBE), Exam. 11.09.2016 (IIIrd Sitting), , 1. If the arcs of square length in, two circles subtend angles of 60°, and 75° at their centres, the ratio of their radii is, (1) 3 : 4, (2) 4 : 5, (3) 5 : 4, (4) 3 : 5, (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 2. The length of the perpendiculars, drawn from any point in the interior of an equilateral triangle to, the respective sides are p1, p2, and p3. The length of each side, of the triangle is, (1), (2), (3), , 35. There is a 4% increase in volume, when a liquid freezes to its solid, state. The percentage decrease, when solid melts to liquid again, is, , (4), , 3, %, 13, , (2) 4%, , (3) 4, , 1, %, 13, , (4) 3, , 11, %, 13, , (SSC CGL Tier-I (CBE), Exam. 11.09.2016 (IInd Sitting), , (3) 14 3 cm, , 2, 3, , b, , b p1 + p2 + p3 g, , 1, p1 + p2 + p 3, 3, , 1, 3, , g, , bp1 + p2 + p3 g, , bp1 + p2 + p3 g, 3, , 4, , (SSC CGL Prelim Exam. 08.02.2004, (First Sitting), , 3. The sides of a triangle are in the, ratio 3 : 4 : 5. The measure of the, largest angle of the triangle is, (1) 60°, (2) 90°, (3) 120°, (4) 150°, (SSC CPO S.I. Exam. 05.09.2004), , SME–1162, , (4), , 14 3, cm, 3, , (SSC CPO S.I. Exam. 26.05.2005), , 5. The base and altitude of a right, angled triangle are 12 cm and 5, cm respectively. The perpendicular distance of its hypotenuse from the opposite vertex is, (1) 4, , 4, cm, 13, , (3) 5 cm, , (2) 4, , 8, cm, 13, , (4) 7 cm, , (SSC Section Officer (Commercial, Audit) Exam. 26.11.2006 (Second, Sitting ), , TYPE - VII, , (SSC CAPFs (CPO) SI & ASI,, Delhi Police Exam. 05.06.2016), (Ist Sitting), , (1) 3, , 1, 2, , 4. From a point within an equilateral triangle, perpendiculars, drawn to the three sides, are 6, cm, 7 cm and 8 cm respectively., the length of the side of the triangle is :, (1) 7 cm, (2) 10.5 cm, , 6. One acute angle of a right angled, triangle is double the other. If, the length of its hypotenuse is 10, cm, then its area is, (1), , 25, 3 cm2 (2) 25 cm2, 2, , (3) 25 3 cm2 (4), , 75, cm2, 2, , (SSC CPO S.I. Exam. 09.11.2008), , 7. In an equilateral triangle ABC of, side 10cm, the side BC is, trisected at D. Then the length (in, cm) of AD is, (1) 3 7, (3), , 10 7, 3, , (2) 7 3, (4), , 7 10, 3, , (SSC CGL Tier-1 Exam. 19.06.2011, (First Sitting), , 8. The perimeter of a triangle is, 40cm and its area is 60 cm2. If, the largest side measures 17cm,, then the length (in cm) of the, smallest side of the triangle is, (1) 4, , (2) 6, , (3) 8, , (4) 15, , (SSC CGL Tier-1 Exam. 26.06.2011, (First Sitting)

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MENSURATION, 9. The ratio of the area of two isosceles triangles having the same, vertical angle (i.e. angle between, equal sides) is 1 : 4. The ratio, of their heights is, (1) 1 : 4, (2) 2 : 5, (3) 1 : 2, (4) 3 : 4, (SSC CPO (SI, ASI & Intelligence, Officer) Exam. 28.08.2011 (Paper-I), , 10. The length of one side of a rhombus is 6.5 cm and its altitude is, 10 cm. If the length of its diagonal be 26 cm, the length of the, other diagonal will be :, (1) 5 cm, (2) 10 cm, (3) 6.5 cm, (4) 26 cm, (SSC CPO S.I. Exam. 26.05.2005), , 11. The measure of each of two opposite angles of a rhombus is 60°, and the measure of one of its, sides is 10cm. The length of its, smaller diagonal is :, (1) 10 cm, , (2) 10 3 cm, , 5, , 15. If the diagonals of a rhombus are, 8 and 6, then the square of its, size is, (1) 25, (2) 55, (3) 64, (4) 36, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 16. One of the four angles of a, rhombus is 60°. If the length of, each side of the rhombus is 8 cm,, then the length of the longer, diagonal is, (1) 8 3 cm, , (2) 8 cm, , (3) 4 3 cm, , (4), , 12. Two adjacent sides of a, parallelogram are of length 15 cm, and 18 cm. If the di stance, between two smaller sides is 12, cm, then the distance between, two bigger sides is, (1) 8 cm, (2) 10 cm, (3) 12 cm, (4) 15 cm, (SSC CHSL DEO & LDC Exam., 04.12.2011 (Ist Sitting (North Zone), , 13. A parallelogram ABCD has sides, AB = 24 cm and AD = 16 cm., The distance between the, sides AB and DC is 10 cm. Find, the distance between the sides, AD and BC., (1) 16 cm., (2) 18 cm., (3) 15 cm., (4) 26 cm., (SSC CHSL DEO & LDC Exam., 04.12.2011 (IInd Sitting (East Zone), , 14. The adjacent sides of a parallelogram are 36 cm and 27 cm in, length. If the distance between, the shorter sides is 12 cm, then, the distance between the longer, sides is, (1) 10 cm, (2) 12 cm, (3) 16 cm, (4) 9 cm, (SSC CHSL DEO & LDC Exam., 11.12.2011 (Ist Sitting (East Zone), , 3, , cm, , (SSC Graduate Level Tier-I, Exam. 21.04.2013), , 17. The diagonals of a rhombus are, 12 cm and 16 cm respectively., The length of one side is, (1) 8 cm, (2) 6 cm, (3) 10 cm, (4) 12 cm, (SSC Graduate Level Tier-II, , 2 cm, (3) 10 2 cm (4), 2, (SSC CPO S.I. Exam. 16.12.2007), , 8, , Exam. 29.09.2013, , 18. Each interior angle of a regular, polygon is 18° more than eight, times an exterior angle. The number of sides of the polygon is, (1) 10, (2) 15, (3) 20, (4) 25, (SSC CPO (SI, ASI & Intelligence, Officer) Exam. 28.08.2011 (Paper-I), , 19. An exterior angle of a regular, polygon is 72°. The sum of all the, interior angles is, (1) 360°, (2) 480°, (3) 520°, (4) 540°, (SSC Graduate Level Tier-I, Exam. 11.11.2012, Ist Sitting), , 20. A cylindrical tank of diameter 35, cm is full of water. If 11 litres, of water is drawn off, the water, level in the tank will drop by :, , FG use p = 22 IJ, H, 7 K, (1) 10, , (1), , 3, cm, 2p, , (2), , (3), , 9, cm, 2p, , (4) 2p cm, , 6, cm, p, , (SSC CGL Prelim Exam. 04.02.2007, (Second Sitting), , 22. The diameter of the base of a, right circular cone is 4 cm and, its height 2 3 cm. The slant, height of the cone is, (1) 5 cm, (2) 4 cm, (3) 2 3 cm, , (4) 3 cm, , (SSC CHSL DEO & LDC Exam., 28.11.2010 (IInd Sitting), , 23. A sector is formed by opening out, a cone of base radius 8 cm and, height 6 cm. Then the radius of, the sector is (in cm), (1) 4, (2) 8, (3) 10, (4) 6, (SSC Delhi Police S.I., (SI) Exam. 19.08.2012), , 24. A right circular cone is 3.6 cm, high and radius of its base is 1.6, cm. It is melted and recast into, a right circular cone with radius, of its base as 1.2 cm. Then the, height of the cone (in cm) is, (1) 3.6, (2) 4.8, (3) 6.4, (4) 7.2, (SSC Graduate Level Tier-II, Exam. 29.09.2013), , 25. A copper sphere of radius 3 cm, is beaten and drawn into a wire, of diameter 0.2 cm. The length, of the wire is :, (1) 9 m, (2) 12 m, (3) 18 m, (4) 36 m, (SSC CPO S.I. Exam. 26.05.2005), , 1, 6, cm. (2) 12 cm., 2, 7, , (3) 14 cm., , 21. A ri ght circu lar cyl ind er i s, formed by rolling a rectangular, paper 12 cm long and 3 cm wide, along its length. The radius of, the base of the cylinder will be, , (4) 11, , 3, cm., 7, , (SSC CGL Prelim Exam. 04.07.1999, (Second Sitting), , SME–1163, , 26. If surface area and volume of a, sphere are S and V respectively,, then value of, (1) 36 units, (3) 18 units, , S3, is, V2, (2) 9 units, (4) 27 units, , (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013)

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MENSURATION, 27. Assume that a drop of water is, spherical and its diameter is onetenth of a cm. A conical glass has, a height equal to the diameter of, its rim. If 32,000 drops of water fill the glass completely, then, the height of the glass (in cm) is, (1) 1, (2) 2, (3) 3, (4) 4, (SSC Graduate Level Tier-II, , 34. A circle is inscribed in a square., An equilateral triangle of side, , 4 3 cm is inscribed in that, circle. The length of the diagonal, of the square (in centimetres) is, (1) 4 2, , (2) 8, , (3) 8 2, , (4) 16, , (SSC CPO S.I. Exam. 05.09.2004), , Exam. 29.09.2013, , 35. The height of an equilateral tri-, , 28. A cistern of capacity 8000 litres, measures externally 3.3 m by 2.6, m by 1.1 m and its walls are 5, cm thick. The thickness of the, bottom is :, (1) 1 m, (2) 1.1 m, (3) 1 dm, (4) 90 cm, , angle is 4 3 cm. The ratio of the, area of its circumcircle to that of, its in-circle is, (1) 2 : 1, (2) 4 : 1, (3) 4 : 3, (4) 3 : 2, , (SSC CGL Prelim Exam. 11.05.2003, (First Sitting), , 29. A cone is cut at mid point of its, height by a frustum parallel to its, base. The ratio between the two, parts of cone would be, (1) 1 : 1, (2) 1 : 8, (3) 1 : 4, (4) 1 : 7, (SSC Section Officer (Commercial, Audit) Exam. 25.09.2005), , 30. The area of a circle of radius 5, is numerically what percent of, its circum ference?, (1) 200%, (2) 225%, (3) 240%, (4) 250%, (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , 31. If the circumference and area of, a circle are numerically equal,, then the diameter is equal to :, (1) area of the circle, (2), , p, 2, , (SSC CGL Prelim Exam. 27.07.2008, (Second Sitting), , 36. A circle is inscribed in a square, whose length of the diagonal is, 12 2 cm. An equilateral triangle is inscribed in that circle., The length of the side of the triangle is, (1) 4 3 cm, , (2) 8 3 cm, , (3) 6 3 cm, , (4) 11 3 cm, , (SSC Assistant Grade-III, Exam. 11.11.2012 (IInd Sitting), , (3) 2p, , (4) 4, , 32. A chord of length 30 cm is at a, distance of 8 cm from the centre of a circle. The radius of the, circle is:, (1) 17 cm, (2) 23 cm, (3) 21 cm, (4) 19 cm, (SSC Graduate Level Tier-I, Exam. 21.04.2013, Ist Sitting), , 33. The circum-radius of an equilateral triangle is 8 cm. The in-radius of the triangle is, (1) 3.25 cm, (2) 3.50 cm, (3) 4 cm, (4) 4.25 cm, (SSC CPO S.I. Exam. 07.09.2003), , which of the folis correct ?, (2) 2h = d, (4) 3h = 2d, , (SSC CPO S.I. Exam. 09.11.2008), , 41. A solid cone of height 9 cm with, diameter of its base 18 cm is cut, out from a wooden solid sphere, of radius 9 cm. The percentage, of wood wasted is :, (1) 25%, (2) 30%, (3) 50%, (4) 75%, (FCI Assistant Grade-III, Exam. 05.02.2012 (Paper-I), , East Zone (IInd Sitting), , 42. Two circles with centres A and, B and radius 2 units touch each, other externally at ‘C’. A third, circle with centre ‘C’ and radius, ‘2’ units meets other two at D, and E. Then the area of the, quadrilateral ABDE is, (1) 2 2 sq. units, (2) 3 3 sq. units, (3) 3 2 sq. units, (4) 2 3 sq. units, (SSC CHSL DEO & LDC Exam., 04.11.2012 (IInd Sitting), , (SSC Multi-Tasking Staff, Exam. 17.03.2013, Ist Sitting), , 43. Two cubes of sides 6 cm each, are kept side by side to form a, rectangular parallelopiped. The, area (in sq. cm) of the whole surface o f the rectangular, parallelopiped is, (1) 432, (2) 360, (3) 396, (4) 340, , 38. The ratio of inradius and circumradius of a square is :, , (SSC Graduate Level Tier-I, Exam. 11.11.2012, Ist Sitting), , 37. The radius of the incircle of a triangle whose sides are 9 cm, 12, cm and 15 cm is, (1) 9 cm, (2) 13 cm, (3) 3 cm, (4) 6 cm, , (1) 1 :, , (SSC CGL Prelim Exam. 27.02.2000, (Second Sitting), , sphere d, then, lowing relation, (1) h = d, (3) 2h = 3d, , (3) 1 : 3, , 2, , (2), , 2 :, , 3, , (4) 1 : 2, , (SSC Graduate Level Tier-I, Exam. 21.04.2013, Ist Sitting), , 39. The perimeter of a rectangle and, a square are 160 m each. The, area of the rectangle is less than, that of the square by 100 sq m., The length of the rectangle is, (1) 30 m, (2) 60 m, (3) 40 m, (4) 50 m, (SSC CGL Prelim Exam. 13.11.2005, (Second Sitting), , 40. The volume of a right circular cylinder and that of a sphere are, equal and their radii are also, equal. If the height of the cylinder be h and the diameter of the, , SME–1164, , 44. The diameter of a copper sphere, is 1 8 cm. The sphere is melted, and is drawn into a long wire of, uniform circular cross-section. If, the length of the wire is 108 m,, the diameter of the wire is, (1) 1 cm, (2) 0.9cm, (3) 0.3 cm, (4) 0.6 cm, (SSC FCI Assistant Grade-III Main, Exam. 07.04.2013), , 45. A river 3 m deep and 40 m wide, is flowing at the rate of 2 km, per hour. How much water (in litres) will fall into the sea in a, minute?, (1) 4,00,000, , (2) 40,00,000, , (3) 40,000, , (4) 4,000, , (SSC CGL Tier-1 Exam. 26.06.2011, (First Sitting)

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MENSURATION, 46. Water is flowing at the rate of 3, km/hr through a circular pipe, of 20 cm internal diameter into, a circular cistern of diameter, 10m and depth 2m. In how, much time will the cistern be, filled ?, (1) 1 hour, (2) 1 hour 40 minutes, (3) 1 hour 20 minutes, (4) 2 hours 40 minutes, (SSC CGL Tier-1 Exam. 26.06.2011, (Second Sitting), , 47. The rain water from a roof 22 m, × 20 m drains into a cylindrical, vessel having a diameter of 2 m, and height 3.5 m. If the vessel, is just full, then the rainfall (in, cm) is :, (1) 2, , (2) 2.5, , (3) 3, , (4) 4.5, (SSC CHSL DEO & LDC, Exam. 27.11.2010), , 48. 2 cm of rain has fallen on a, square km of land. Assuming, that 50% of the raindrops could, have been collected and contained in a pool having a 100 m, × 10 m base, by what level, would the water level in the pool, have increased ?, (1) 1 km, (2) 10 m, (3) 10 cm, (4) 1 m, (SSC Graduate Level Tier-II, Exam.16.09.2012), , 49. A parallelopiped whose sides are, in ratio 2 : 4 : 8 have the same, volume as a cube. The ratio of, their surface area is :, (1) 7 : 5, (2) 4 : 3, (3) 8 : 5, (4) 7 : 6, (SSC CHSL DEO & LDC, Exam. 21.10.2012 (IInd Sitting), , 50. If two adjacent sides of a rectangular parallelopiped are 1 cm, and 2 cm and the total surface, area of the parallelopiped is 22, square cm, then the diagonal of, the parallelopiped is, (1), , 10 cm, , (2) 2 3 cm, , (3), , 14 cm, , (4) 4cm, , (SSC CHSL DEO & LDC, Exam. 04.11.2012 (IInd Sitting), , 51. What part of a ditch, 48 metres, long, 16.5 metres broad and 4, metres deep can be filled by the, earth got by digging a cylindrical tunnel of diameter 4 metres, and length 56 metres ? (Use p, =, , 22, ), 7, , (1), , 1, 9, , (2), , 2, 9, , (3), , 7, 9, , (4), , 8, 9, , (SSC CGL Prelim Exam. 04.02.2007, (First Sitting), , 52. The perimeters of a circle, a, square and an equilateral triangle, are same and their areas are C,, S and T respectively. Which of, the following statement is true ?, (1) C = S = T, (2) C > S > T, (3) C < S < T, (4) S < C < T, (SSC CGL Tier-I Exam., 19.10.2014 (Ist Sitting), , 53. The base of a right prism is a, quadrilateral ABCD. Given that, AB = 9 cm, BC = 14 cm, CD =, 13 cm, DA = 12 cm and ÐDAB, = 90°. If the volume of the prism, be 2070 cm3, then the area of, the lateral surface is, (1) 720 cm2, (2) 810 cm2, 2, (3) 1260 cm (4) 2070 cm2, (SSC CGL Tier-I Exam. 19.10.2014), , 54. An elephant of length 4 m is at, one corner of a rectangular cage, of size (16 m × 30 m) and faces, towards the diagonally opposite, corner. If the elephant starts, moving towards the diagonally, opposite corner it takes 15 seconds to reach this corner. Find, the speed of the elephant., (1) 1 m/sec, (2) 2 m/sec, (3) 1.87 m/sec (4) 1.5 m/sec, (SSC CHSL DEO & LDC Exam., 02.11.2014 (IInd Sitting), , 55. A horse takes 2, , 1, seconds to, 2, , complete a round around a circular field. If the speed of the, horse was 66 m/sec, then the, radius of the field is,, [Given p =, , 22, ], 7, , (1) 25.62 m, (3) 25.26 m, , (2) 26.52 m, (4) 26.25 m, , (SSC CHSL DEO & LDC, Exam. 9.11.2014), , SME–1165, , 56. The diameter of the front wheel, of an engine is 2x cm and that, of rear wheel is 2y cm. To cover, the same distance, find the number of times the rear wheel will, revolve when the front wheel revolves ‘n’ times., , n, , (1) xy times, , nx, , (3) y, , times, , (2), , yn, times, x, , (4), , xy, times, n, , (SSC CHSL DEO Exam. 02.11.2014, (Ist Sitting), , 57. A bicycle wheel has a diameter, (including the tyre) of 56 cm. The, number of times the wheel will, rotate to cover a distance of 2.2, km is (Assume p =, , 22, ), 7, , (1) 625, , (2) 1250, , (3) 1875, , (4) 2500, , (SSC CHSL DEO Exam. 16.11.2014, (Ist Sitting), , 58. If one diagonal of a rhombus of, side 13 cm is 10 cm, then the, other diagonal is, (1) 24 cm, , (2) 20 cm, , (3) 16 cm, , (4) 28 cm, , (SSC CHSL (10+2) DEO & LDC, Exam. 16.11.2014 , Ist Sitting, TF No. 333 LO 2), , 59. A brick 2" thick is placed against, a wheel to act for a stop. The, horizontal distance of the face of, the brick from the point where, the wheel touches the ground is, 6". The radius of the wheel in, inches is, (1) 10, , (2) 5, , (3) 12, , (4) 6, , (SSC CHSL (10+2) DEO & LDC, Exam. 16.11.2014, IInd Sitting, TF No. 545 QP 6), , 60. A solid has 12 vertices and 30, edges. How many faces does it, have?, (1) 22, (2) 24, (3) 26, (4) 20, (SSC CHSL (10+2) Tier-I (CBE), Exam. 15.01.2017) (IInd Sitting)

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MENSURATION, 157. (2) 158. (2) 159. (1) 160. (2), , SHORT ANSWERS, , TYPE-II, , 161. (2) 162. (4) 163. (3) 164. (4), , TYPE-I, , 165. (4) 166. (1) 167. (1) 168. (3), , 1. (2), , 2. (1), , 3. (3), , 4. (2), , 169. (3) 170. (3) 171. (3) 172. (2), , 5. (2), , 6. (3), , 7. (2), , 8. (4), , 1. (2), , 2. (3), , 3. (4), , 4. (3), , 173. (3) 174. (2) 175. (1) 176. (4), , 9. (3), , 10. (1), , 11. (4), , 12. (3), , 5. (2), , 6. (3), , 7. (3), , 8. (2), , 177. (1) 178. (2) 179. (2) 180. (2), , 13. (1), , 14. (3), , 15. (3), , 16. (4), , 9. (2), , 10. (4), , 11. (1), , 12. (1), , 181. (3) 182. (4) 183. (2) 184. (3), , 17. (3), , 18. (1), , 19. (3), , 20. (3), , 13. (1), , 14. (1), , 15. (2), , 16. (4), , 185. (1) 186. (4) 187. (2) 188. (3), , 21. (1), , 22. (1), , 23. (3), , 24. (1), , 17. (4), , 18. (3), , 19. (4), , 20. (1), , 189. (3) 190. (2) 191. (2) 192. (4), , 25. (4), , 26. (1), , 27. (4), , 28. (3), , 21. (2), , 22. (2), , 23. (3), , 24. (1), , 25. (3), , 26. (1), , 27. (1), , 28. (4), , 193. (1) 194. (4) 195. (1) 196. (3), , 29. (3), , 30. (1), , 31. (2), , 32. (1), , 29. (4), , 30. (4), , 31. (2), , 32. (3), , 197. (4) 198. (3) 199. (1) 200. (4), , 33. (2), , 34. (3), , 35. (2), , 36. (2), , 33. (3), , 34. (3), , 35. (2), , 36. (3), , 201. (1) 202. (1) 203. (4) 204. (2), , 37. (1), , 38. (1), , 39. (1), , 40. (2), , 37. (3), , 38. (3), , 39. (3), , 40. (2), , 205. (*), , 206. (3) 207. (2) 208. (2), , 41. (4), , 42. (3), , 43. (2), , 44. (2), , 41. (4), , 42. (3), , 43. (1), , 44. (3), , 209. (1) 210. (2) 211. (2) 212. (2), , 45. (3), , 46. (1), , 47. (2), , 48. (2), , 45. (4), , 46. (4), , 47. (2), , 48. (1), , 213. (1) 214. (2) 215. (3) 216. (3), , 49. (2), , 50. (3), , 51. (2), , 52. (1), , 49. (4), , 50. (3), , 51. (1), , 52. (3), , 217. (3) 218. (1) 219. (3) 220. (3), , 53. (2), , 54. (1), , 55. (4), , 56. (1), , 53. (3), , 54. (2), , 55. (2), , 56. (1), , 221. (3) 222. (4) 223. (4) 224. (1), , 57. (2), , 58. (3), , 59. (3), , 60. (3), , 57. (3), , 58. (3), , 59. (2), , 60. (3), , 225. (1) 226. (3) 227. (2) 228. (3), , 61. (2), , 62. (3), , 63. (2), , 64. (4), , 61. (3), , 62. (4), , 63. (4), , 64. (2), , 229. (3) 230. (1) 231. (1) 232. (2), , 65. (1), , 66. (3), , 67. (4), , 68. (2), , 65. (1), , 66. (2), , 67. (3), , 68. (3), , 233. (3) 234. (4) 235. (3) 236. (2), , 69. (1), , 70. (1), , 71. (3), , 72. (1), , 74. (1), , 75. (1), , 76. (1), , 69. (4), , 70. (3), , 71. (2), , 72. (2), , 237. (1) 238. (4) 239. (4) 240. (2), , 73. (3), 77. (1), , 78. (2), , 79. (2), , 80. (2), , 73. (4), , 74. (4), , 75. (4), , 76. (3), , 81. (2), , 82. (2), , 83. (1), , 84. (3), , 77. (4), , 78. (1), , 79. (4), , 80. (1), , 81. (1), , 82. (3), , 83. (3), , 84. (2), , 249. (2) 250. (2) 251. (4) 252. (3), , 85. (1), , 86. (2), , 87. (3), , 88. (1), , 85. (4), , 86. (3), , 87. (2), , 88. (2), , 253. (4) 254. (2) 255. (2) 256. (3), , 89. (2), , 90. (3), , 91. (3), , 92. (4), , 89. (1), , 90. (2), , 91. (2), , 92. (2), , 257. (4) 258. (3) 259. (1) 260. (2), , 93. (2), , 94. (3), , 95. (2), , 96. (3), , 93. (1), , 94. (3), , 95. (3), , 96. (1), , 97. (3), , 98. (1), , 99. (2) 100. (1), , 241. (4) 242. (3) 243. (4) 244. (2), 245. (2) 246. (1) 247. (4) 248. (4), , 261. (1) 262. (1) 263. (3) 264. (1), , 101. (4) 102. (2) 103. (2), , 99. (4) 100. (2), , 265. (2) 266. (2) 267. (4) 268. (3), , 101. (1) 102. (1) 103. (4) 104. (1), , 269. (4) 270. (2) 271. (3) 272. (1), , 105. (1) 106. (3) 107. (1) 108. (4), , 273. (2) 274. (3) 275. (2) 276. (1), , 109. (4) 110. (3) 111. (1) 112. (2), , 277. (1) 278. (4) 279. (4) 280. (2), , 1. (4), , 2. (2), , 3. (3), , 4. (3), , 113. (1) 114. (1) 115. (2) 116. (2), , 281. (2) 282. (4) 283. (4) 284. (3), , 5. (4), , 6. (1), , 7. (4), , 8. (1), , 117. (3) 118. (3) 119. (4) 120. (2), , 285. (4) 286. (4) 287. (4) 288. (3), , 9. (4), , 10. (4), , 11. (3), , 12. (4), , 121. (3) 122. (2) 123. (1) 124. (2), , 289. (2) 290. (2) 291. (3) 292. (1), , 13. (4), , 14. (4), , 15. (2), , 125. (4) 126. (3) 127. (3) 128. (3), , 293. (2) 294. (2) 295. (1) 296. (1), , 129. (2) 130. (2) 131. (4) 132. (2), , 297. (4) 298. (2) 299. (1) 300. (1), , 133. (1) 134. (2) 135. (2) 136. (4), , 301. (1) 302. (3) 303. (2) 304. (4), , 1. (2), , 2. (1), , 3. (1), , 4. (1), , 137. (3) 138. (3) 139. (4) 140. (2), , 305. (2) 306. (4) 307. (3) 308. (1), , 5. (4), , 6. (2), , 7. (4), , 8. (3), , 141. (3) 142. (3) 143. (2) 144. (4), , 309. (3) 310. (1) 311. (2) 312. (2), , 9. (1), , 10. (2), , 11. (2), , 12. (3), , 145. (3) 146. (2) 147. (3) 148. (2), , 313. (1) 314. (3) 315. (2) 316. (3), , 13. (1), , 14. (2), , 15. (1), , 16. (1), , 149. (3) 150. (4) 151. (4) 152. (1), , 317. (1) 318. (2) 319. (2) 320. (3), , 17. (4), , 18. (3), , 19. (1), , 20. (1), , 153. (2) 154. (2) 155. (3) 156. (4), , 321. (1), , 21. (3), , 22. (1), , 23. (2), , 24. (4), , 97. (1), , 98. (1), , SME–1166, , TYPE-III, , TYPE-IV

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MENSURATION, 25. (4), , 26. (4), , 27. (1), , 28. (1), , 193. (4) 194. (1) 195. (3) 196. (2), , 85. (2), , 86. (3), , 87. (3), , 88. (4), , 29. (3), , 30. (3), , 31. (2), , 32. (1), , 197. (3) 198. (3) 199. (2) 200. (4), , 89. (1), , 90. (1), , 91. (4), , 92. (3), , 33. (1), , 34. (4), , 35. (1), , 36. (4), , 201. (4) 202. (1) 203. (4) 204. (4), , 93. (4), , 94. (4), , 95. (4), , 96. (4), , 37. (4), , 38. (2), , 39. (3), , 40. (2), , 205. (3) 206. (2) 207. (4) 208. (4), , 97. (3), , 98. (4), , 99. (1) 100. (4), , 41. (3), , 42. (4), , 43. (1), , 44. (1), , 209. (2) 210. (1) 211. (1) 212. (2), , 101. (3) 102. (1) 103. (4) 104. (4), , 45. (2), , 46. (4), , 47. (4), , 48. (4), , 213. (1) 214. (2) 215. (3) 216. (1), , 105. (3) 106. (4) 107. (1) 108. (4), , 49. (2), , 50. (3), , 51. (1), , 52. (4), , 217. (4) 218. (4) 219. (3) 220. (1), , 109. (3) 110. (2) 111. (1) 112. (2), , 53. (1), , 54. (3), , 55. (2), , 56. (1), , 221. (4) 222. (2) 223. (3) 224. (4), , 57. (2), , 58. (3), , 59. (2), , 60. (3), , 113. (3) 114. (2) 115. (2) 116. (1), , 225. (2) 226. (3) 227. (3) 228. (4), , 61. (4), , 62. (2), , 63. (3), , 64. (2), , 117. (4) 118. (2) 119. (1) 120. (3), , 65. (4), , 66. (4), , 67. (2), , 68. (4), , 69. (3), , 70. (4), , 71. (1), , 72. (1), , 73. (3), , 74. (3), , 75. (3), , 76. (3), , 77. (3), , 78. (2), , 79. (4), , 80. (1), , 81. (1), , 82. (3), , 83. (2), , 84. (2), , 85. (2), , 86. (2), , 87. (1), , 88. (3), , 89. (1), , 90. (3), , 91. (1), , 92. (1), , 93. (2), , 94. (4), , 95. (3), , 96. (2), , 97. (3), , 98. (3), , 99. (3) 100. (2), , 229. (4) 230. (3) 231. (4) 232. (3), , 121. (2) 122. (3) 123. (1) 124. (3), , 233. (2) 234. (4) 235. (3) 236. (1), , 125. (3) 126. (1) 127. (2) 128. (3), , 237. (3) 238. (1) 239. (3) 240. (3), , TYPE-VI, , 241. (4) 242. (4) 243. (3) 244. (3), 245. (1) 246. (3) 247. (2) 248. (4), , 1. (1), , 2. (1), , 3. (2), , 4. (3), , 249. (1) 250. (1) 251. (4) 252. (2), , 5. (3), , 6. (3), , 7. (4), , 8. (1), , 253. (1) 254. (2) 255. (1) 256. (4), , 9. (3), , 10. (2), , 11. (4), , 12. (2), , 257. (4) 258. (2) 259. (1) 260. (4), , 13. (4), , 14. (1, , 15. (1), , 16. (4), , 261. (4), , 17. (4), , 18. (1), , 19. (4), , 20. (1), , 21. (1), , 22. (4), , 23. (4), , 24. (4), , 25. (1), , 26. (4), , 27. (4), , 28. (4), , 29. (2), , 30. (4), , 31. (4), , 32. (2), , 34. (3), , 35. (4), , 36. (1), , 101. (2) 102. (2) 103. (2) 104. (4), , TYPE-V, , 105. (2) 106. (1) 107. (3) 108. (1), 1. (4), , 2. (2), , 3. (1), , 4. (2), , 113. (4) 114. (3) 115. (1) 116. (1), , 5. (1), , 6. (1), , 7. (1), , 8. (1), , 33. (3), , 117. (2) 118. (1) 119. (4) 120. (2), , 9. (3), , 10. (3), , 11. (3), , 12. (3), , 37. (4), , 121. (2) 122. (3) 123. (2) 124. (1), , 13. (1), , 14. (2), , 15. (4), , 16. (3), , 125. (4) 126. (4) 127. (4) 128. (3), , 17. (4), , 18. (3), , 19. (2), , 20. (2), , 129. (2) 130. (1) 131. (3) 132. (2), , 21. (1), , 22. (4), , 23. (3), , 24. (3), , 1. (3), , 2. (1), , 3. (2), , 4. (3), , 133. (1) 134. (4) 135. (2) 136. (3), , 25. (2), , 26. (3), , 27. (2), , 28. (4), , 5. (2), , 6. (1), , 7. (3), , 8. (3), , 137. (2) 138. (4) 139. (4) 140. (2), , 29. (2), , 30. (3), , 31. (3), , 32. (3), , 9. (3), , 10. (1), , 11. (1), , 12. (2), , 141. (2) 142. (1) 143. (4) 144. (2), , 33. (2), , 34. (2), , 35. (1), , 36. (3), , 13. (3), , 14. (4), , 15. (1), , 16. (1), , 145. (3) 146. (4) 147. (1) 148. (3), , 37. (4), , 38. (2), , 39. (4), , 40. (4), , 17. (3), , 18. (3), , 19. (4), , 20. (4), , 149. (1) 150. (1) 151. (1) 152. (1), , 41. (4), , 42. (4), , 43. (2), , 44. (2), , 21. (2), , 22. (2), , 23. (3), , 24. (3), , 153. (4) 154. (2) 155. (2) 156. (1), , 45. (3), , 46. (3), , 47. (2), , 48. (3), , 25. (4), , 26. (1), , 27. (4), , 28. (3), , 157. (1) 158. (4) 159. (4) 160. (1), , 49. (4), , 50. (3), , 51. (2), , 52. (1), , 29. (4), , 30. (4), , 31. (4), , 32. (1), , 161. (3) 162. (3) 163. (4) 164. (1), , 53. (1), , 54. (4), , 55. (3), , 56. (3), , 33. (3), , 34. (3), , 35. (2), , 36. (3), , 165. (2) 166. (4) 167. (*) 168. (2), , 57. (2), , 58. (3), , 59. (3), , 60. (2), , 37. (3), , 38. (1), , 39. (4), , 40. (4), , 169. (4) 170. (4) 171. (3) 172. (3), , 61. (1), , 62. (4), , 63. (1), , 64. (4), , 41. (4), , 42. (2), , 43. (2), , 44. (4), , 173. (1) 174. (*), , 175. (1) 176. (1), , 65. (4), , 66. (2), , 67. (1), , 68. (2), , 70. (2), , 71. (1), , 72. (3), , 46. (2), , 47. (2), , 48. (2), , 177. (1) 178. (4) 179. (1) 180. (1), , 69. (4), , 45. (2), , 73. (1), , 74. (3), , 75. (2), , 76. (1), , 49. (4), , 50. (3), , 51. (2), , 52. (2), , 181. (3) 182. (3) 183. (2) 184. (2), 185. (4) 186. (4) 187. (3) 188. (2), , 77. (4), , 78. (4), , 79. (2), , 80. (2), , 53. (1), , 54. (2), , 55. (4), , 56. (3), , 189. (1) 190. (3) 191. (3) 192. (1), , 81. (3), , 82. (3), , 83. (3), , 84. (2), , 57. (2), , 58. (1), , 59. (4), , 60. (4), , 109. (4) 110. (4) 111. (4) 112. (2), , SME–1167, , TYPE-VII