A cone and hemisphere have the same base and the same height. Fin… - Vidyadip

Question

A cone and hemisphere have the same base and the same height. Find the ratio between theirvolumes.

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Answer

Let the radius of base be $'r\ '$ and the height be $'h\ '$
Volume of cone, $V_c$
$=\frac{1}{3} \pi r^2 h$
Volume of hemisphere, $V_h$
$=\frac{2}{3} \pi r^2 h$
$\frac{V_c}{V_h}=\frac{\frac{1}{3} \pi r^2 r}{\frac{2}{3} \pi r^3}$
$\Rightarrow \frac{V_c}{V_h}=\frac{1}{2}$

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