Test Details

Surface Areas and Volumes

Solve all question carefully

Jan 31, 8:00 PM

95 minutes

Jan 31, 9:35 PM

50.0 marks

MCQ

15 questions

Vipin Sir

Efficiency in Mechanical Engineering 4year Teaching experience for Mathematics and Science (CBSC + UP Board). 2times selected in Airforce. 3times in selected in Navy.

Class Details

Mathematics

Class X Term 2

Mathematics

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Question Text

Question 1 :
Find the curved surface area of frustum coneradii 2.5 and 1.2 cm and a slant height 12.5 cm.

Question 2 :
The curved surface area of frustum cone is 400 $m^2$The diameter of a cone is 0.5 and 2 m.Find the slant height. (Use $\pi$ = 3.14).

Question 3 :
Thevolume of the frustum of a cone is 54 cm$^3$ and its height is 6 cm, bottomradius, R = 1 cm. Find its top radius, r. (Use $\pi$= 3).

Question 4 :
Diameter of the base of a cone is $10.5cm$ and its slant height is $10cm$. Find its curved surface area.

Question 5 :
The diameters of the two circular ends of the bucket are $44 $ cm and $24 $ cm. The height of the bucket is $35$ cm. The capacity of the bucket is<br/>

Question 6 :
A medicine-capsule is in the shape of a cylinder ofdiameter 0.5 cm with two hemisphere stuck to each of its ends. The length of entire capsule is 2 cm The capacity of the capsule is

Question 7 :
A vessel is in the form of a frusturn of a cone of height $21$ cm with radii of its lower and upper ends as $8$ cm and 18 cm respectively. Find the cost of milk which can completely fill the vessel at the rate of Rs. $10$ per litre.

Question 8 :
Three solid cubes have a face diagonal of $\displaystyle 4\sqrt{2}$ cm each. Three other solid cubes have a face diagonal of $\displaystyle 8\sqrt{2}$ cm each. All the cubes are melted together to from a big cube. Find the side of the cube formed (in cm).

Question 9 :
A solid sphere of radius $x$ cm is melted and cast into a shape of a solid cone of radius $x$ cm. The height of the cone is:<br/>

Question 10 :
A cube whose volume is $1/8$ cubic centimeter is placed on top of a cube whose volume is $1{cm}^{3}$. The two cubes are then placed on top of a third cube whose volume is $8{Cm}^{3}$. The height of the stacked cubes is

Question 11 :
A solid sphere of radius 6 mm is melted and then cast into small spherical balls each of radius 0.6 mm. Find the number of balls thus obtained.

Question 12 :
A sphere of radius $r$ lies inside a cube and touches each of the six sides of the cube. Calculate the volume of the cube in terms of $r$.

Question 13 :
<p>A tent of height16 m is in the form of right circular cylinder with radius of base 2 m andheight 6 m, surmounted by a right circular cone of the same base. Find the costof the canvas of the tent at the rate of Rs. 100 per m.</p>

Question 14 :
Solid cylinders of equal volume are tightly packed in two layers in a rectangular box such that in each layer there are three rows of four such cylinders Find the percentage of volume of empty space in the box approximately.

Question 15 :
The shape of thewooden block is of the form of frustum of a cone.Determine the volumeof a frustum of a cone if the diameters of the ends are 15 cm and 3 cm and itsperpendicular height is 18 cm.

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