CBSE Class 10-Mathematics: Chapter –13 Surface Areas and Volumes Part 11
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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 sphereThen
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 hemisphereVolume of cone