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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.3 in Chapter 17 - Mensuration
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Write whether the following statements are true or false. Justify your answer :
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.
Answer:
Solution:
Here, it is given that a cone, a hemisphere and a cylinder stand on equal bases and have the same height.
Let r be radius of cone, hemisphere and cylinder.
So the height of the cone = r
Height of cylinder = r
Volume of cone = (1/3)π r2h
= (1/3)π r3
Volume of hemisphere = (2/3)π r3
Volume of cylinder = π r2h
=π r3
Ratio of volume of cone , hemisphere and cylinder = (1/3)π r3 : (2/3)π r3 : π r3
= 1/3 : 2/3 : 1
= 1:2:3
Hence the given statement is true. 
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