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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 respective volume is


Solution

Volume of cone $$=\dfrac { 1 }{ 3 } \pi { r }^{ 2 }h$$
Volume of cylinder $$=\pi { r }^{ 2 }h$$
Volume of hemisphere $$=\dfrac { 2 }{ 3 } \pi { r }^{ 3 }$$
These stand on common base & of same height, so that $$r=h$$
Now, $$\dfrac { 1 }{ 3 } \pi { r }^{ 3 }:\dfrac { 2 }{ 3 } \pi { r }^{ 3 }:\pi { r }^{ 3 }=1:2:3$$

Mathematics

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