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Question
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.
Options
True
False
Solution
This statement is True.
Explanation:
Let radius of hemisphere is r.
Volume of a cone, V1 = `1/3` πr2h
V1 = `1/3` πr2(r) ...[∴ h = r]
= `1/3` πr3
Volume of a hemisphere, V2 = `2/3` πr3
Volume of cylinder, V3 = πr2h = πr2 × r = πr3 ...[∴ h = r]
V1 : V2 : V3 = `1/2` πr3 : `2/3` πr3 : πr3 = 1 : 2 : 3
Hence, the ratio of their volumes is 1 : 2 : 3.
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