CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 11 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 16:

A cistern, internally measuring has of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being ?


Volume of cistern

Volume of water = 129600 cm3

Volume of cistern to be filled

Volume of a brick

Let bricks be needed. Then, water absorbed by bricks

Question 17:

In one fortnight of a given month, there was a rainfall of in a river valley. If the area of the valley is , show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each long, wide and deep.


Volume of rainfall

Volume of three rivers

Hence, the two are not equivalent.

Question 18:

An oil funnel made of tin sheet consists of a long cylindrical portion attached to a frustum of a cone. If the total height is , diameter of the cylindrical portion is and the diameter of the top of the funnel is , find the area of the tin sheet required to make the funnel (see figure) .


Slant height of the frustum of the cone

Area of the tin sheet required CSA of cylinder CSA of the frustum

Question 19:

Determine the ratio of the volume of a cube to that of a sphere which with exactly fit inside the cube.


Let the radius of the sphere which fits exactly into a cube be r units. Then length of each edge of cube units

Let and be the volumes of the cube and sphere Then

Question 20:

Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r.


Radius of cone radius of hemisphere

Height of cone = radius of hemisphere Volume of cone