CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 11 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 ?

Answer:

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.

Answer:

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) .

Answer:

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.

Answer:

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.

Answer:

Radius of cone radius of hemisphere

Height of cone = radius of hemisphere Volume of cone