Page 1 : VIVEKANANDA RESIDENTIAL SCHOOL, ( Affiliated to C.B.S.E., Delhi – School Code No. 130052 ), Vivekanandapuri, Karimnagar – 505001 (T.S.) 0878 – 2222768 / 2222769, e-mail :
[email protected] URL : www.vrschool.com, , CASE STUDY, Class: IX (Mathematics), , Topic: Surface Areas & Volumes, CASE STUDY-1, , Read the Source/Text given below and answer questions:, Mathematics teacher of a school took her 9th standard students to show Red fort., It wasa part of their Educational trip. The teacher had interest in history as well. She, narrated the facts of Red fort to students. Then the teacher said in this monument, one can find combination of solid figures. There are 2 pillars which are cylindrical in, shape. Also 2 domes at the corners which are hemispherical.7 smaller domes at the, centre. Flaghoisting ceremony on Independence Day takes place near these domes., , *******
Page 2 :
CASE STUDY-2, Read the Source/Text given below and answer questions:, Mathematics teacher of Vivekananda Residential School took IX Class students to, show Gol Gumbaz. It was a part of their Educational trip. The teacher had interest in, history as well. She narrated the facts of Gol Gumbaz to students. Gol Gumbaz is the, tomb of king Muhammad Adil Shah, Adil Shah Dynasty. Construction of the tomb,, located in Vijayapura , Karnataka, India, was started in 1626 and completed in 1656., It reaches up to 51 meters in height while the giant dome has an external diameter, of 44 meters, making it one of the largest domes ever built. At each of the four, corners of the cube is a dome shaped octagonal tower seven stories high with a, staircase inside., , 1. What is the total surface area of a cuboid?, (a) lb + bh + hl, , (b) 2(lb + bh + hl), , (c) 2(lb + bh), , 2, 2, 2, (d) 1 + b + h, , 2. What is the curved surface area of hemispherical dome ?, 2, 2, 2, 2, (a) 908n m, (b) 968n m, (c) 340n m, (d) 780n m, 3. What is the height of the cubodial part?, (a) 14 m, (b) 7 m, (c) 29 m, (d) 18 m, 4. What is the circumference of the base of the dome?, (a) 34∏, (b) 22∏, (c) 44∏, (d) 55∏, , *******, CASE STUDY-3, Read the Source/Text given below and answer questions:, An architect's planned design for a room with dimensions of 8.6 m, 5.4 m and 4 m, respectively. He also planned to make 4 windows with blue colour and 2 doors with, brown wood colour. The room needs to be painted with Asian paint of Green colour, except for the floor and square tiles were used for flooring as shown in the below, figure:
Page 3 :
1. The total area of the four walls is ________., (a) 112 sq m, , (b) 212 sq m, , (c) 312 sq m, , (d) 412 sq m, , 2. If the area of windows and doors is 22 sq m. The area of, the walls to be painted is ____________., (a) 100 sq m, , (b) 110 sq m, , (c) 90 sq m, , (d) 132 sq m, , 3. What is the area of the tiles to be used for flooring?, (a) 64.6 sq m, , (b) 46.44 sq m, , (c) 66.4 sq m, , (d) 44.6 sq m, , 4. The total area of the room is (including windows and doors):, (a) 48.02 sq m, , (b) 840.4 sq m, , (c) 402.8 sq m, , (d) 204.88 sq m, , 5. What is the volume of the air in the room?, (a) 157.68 cu. m, , (b) 168.57 cu. m, , (c) 158.67 cu. m, , (d) 185.76 cu. M, , *******, CASE STUDY-4, Read the Source/Text given below and answer questions:, Mrs. Anu, a Mathematics teacher brings some green coloured clay in the classroom to, teach the topic 'mensuration'. First, he forms a cylinder of radius 6 cm and height 8, cm with the clay. Then, he moulds that cylinder into a sphere similarly; he moulds the, sphere in other different shapes. Answer the following questions:, , *******
Page 4 :
CASE STUDY-5, Read the Source/Text given below and answer questions:, Radha lives in Telangana. Those were very hot days of May. She thought that if we, human beings need so much of water to drink, won’t the birds also be thirsty. He, decided to prepare a vessel to provide water for birds. She found a flexible blue, coloured plastic rectangular sheet 44 cm X 15 cm. He rolled it along its length and, joined the two opposite ends using a tape. She wanted to have a circular base for this, cylinder and searched for another sheet. She found a square sheet 15 cmX15 cm., She got a circular sheet just equal to the base of the cylinder cut from it. 15cm X 44, cm & 15 cm X 15 cm., , 1. The curved surface area of the cylinder formed is _______., (a) 540 cm², , (b) 560 cm², , (c) 640 cm², , (d) 660 cm²., , 2. The radius of the base of the cylinder is ___________., (a) 2 cm, , (b) 3.5 cm, , (c) 7 cm, , (d) 10 cm, , 3. The area of the circular base required for the cylinder is _________., (a) 154 cm², , (b) 216 cm², , (c) 260 cm², , (d) 308 cm², , 4. How much will be the area of square sheet left unused after removing the circular, base of the cylinder from it?, (a) 71 cm², , (b) 21 cm², , (c) 61 cm², , (d) 81 cm², , 5. Find the volume of water that can be filled in the cylinder., (a) 2310 cu. m, , (b) 16857 cu. m, , (c) 15867 cu. m (d) 18576 cu. m, , *******, CASE STUDY-6, Read the Source/Text given below and answer questions:, Mathematics teacher of a school took his 9th standard students to show Taj Mahal. It, was a part of their Educational trip. The teacher had interest in history as well. He, narrated the facts of Taj Mahal to the students. Then the teacher said in this
Page 5 :
monument one can find combination of solid figures. There are 4 pillars which are, cylindrical in shape. Also, 2 domes at the back side which are hemispherical. 1 big, domes at the centre. It is the finest example of the symmetry. (Use π = 22/7), 1. How much cloth material will be required to cover, two small domes each of radius 4.2 metres?, (a) 52.08 cm2, (b) 52.8 m2, (c) 52 m2 (d) none, 2. Write the formula to find the volume of one pillar, (including hemispherical dome)., (a) πr2(l + r), (b) πr2(2/3 r + h), (c) 2πr2h, (d) none, 3. The volume of the hemispherical dome at the centre if base radius is 7 m is _____., (a) 718.66 cm3, (b) 152.8 m3, (c) 718.66 m3, (d) 56 m3, 4. What is the lateral surface area of all 4 pillars if height of the each pillar is 14 m, and base radius is 1.4 m (without dome)?, (a) 508 m2, (b) 591.36 m2, (c) 52 m2, (d) none, 5. The cost of polishing all the four pillars if the cost of 1 m2 is Rs. 270, will be ____., (a) Rs. 1,59,667.20, , (b) Rs. 2,00,000, , (c) Rs. 1,52,567.50, , (d) none, , *******, CASE STUDY-7, Read the Source/Text given below and answer questions:, In a newly constructed park which is situated in the heart of city Karimnagar, an, architect has form a structure in the given shape. The shape has a cuboid, which is, standing on the two cylindrical beams. The dimensions of the cuboid are 1.5 m, 3 m, and 0.5 m. The dimensions of the cylinders are of height 2 m and diameter 0.6 m., , *******
Page 6 :
CASE STUDY-8, Read the Source/Text given below and answer questions:, One day teacher planned to take all the Class IX students to the milk factory, (Chilling plant) and asked the students to observe it carefully. Refer to this plant, its, machinery is shown below. It is related to some solid shapes, which we study in our, curriculum., , *******
