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.
Solution:
True
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 x 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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