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Question
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.
Solution
Given that,
A cone, hemisphere and a cylinder stand one equal bases and have the same weight
We know that
`V_"cone ": V_"hemispere" : V_"cylinder"`
⇒ `1/3πr^2h:2/3πr^3:πr^2h`
Multiplying by 3
⇒ ` π r^2 h : 2πr^3 : 3πr^2h`or
`πr^3 : 2πr^3 : 3πr^3 [∴ r=h ∵ r^2 h = r^3]`
Or 1:2:3
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