CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Problems Based on Conversion of Solids

Question 1:

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is and the height of the cone is . The solid is placed in a cylindrical tub, full of water, in such a way that the whole solid is submerged in water. If the radius of the cylindrical tub is and its height is find the volume of water left in the cylindrical tub.


No. of solid of of hemisphere

On substituting we get,


On substituting we get,

Volume of left in the cylinder

Question 2:

A bucket of height and made up of copper sheet is in the form of frustum of right circular cone with radii of its lower and upper ends as and respectively. Calculate

i. the height of the cone of which the bucket is a part

ii. the volume of water which can be filled in the bucket

iii. the area of copper sheer required to make the bucket


Let total height be h

of cone which bucket is a part

Substitute to get Ans. : ii) iii)

Question 3:

A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is


S. A. of sphere = S. A of cube

ratio of their volume

On simplifying & substituting, we get

Question 4:

A right triangle whose sides are is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed.


Apply to right to get

Find the Volume and Surface Area

Vol of double

SA of double cone

Question 5:

Water in a canal wide and deep is flowing with a velocity of . How much area will it irrigate in minutes if of standing water is required for irrigation?


Width of canal

Depth of canal


Length of water column is formed in

Let of area be irrigated

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