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Question

Question 7
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.


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Solution

True.
Let the radius of the hemisphere be r.

Volume of the cone, V1=13πr2h

V1=13πr2(r) [h=r]

=13πr3

Now, Volume of the hemisphere, V2=23πr3

And volume of the cylinder, V3=πr2h=πr2×r=πr3 [h=r]

V1:V2:V3=13πr3:23πr3:πr3=1:2:3

Hence, the ratio of their volumes is 1:2:3.


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