### If a hemisphere and a cylinder stand on equal base and have the same height, find the ratio of their volumes.

$2:3$
1. The volume of a cylinder of radius $r$ and height $h$ is $\pi r^2h.$
2. The volume of a hemisphere of radius $r$ is $\dfrac {2} {3} \pi r^3$.
3. \begin{align} \dfrac { \text { Volume of hemisphere } } { \text { Volume of cylinder } } & = \dfrac { \dfrac {2} {3} \pi r^3 }{ \pi r^2h } \space [\because r = h] \\ & = \dfrac { 2 } { 3 } \end{align}
So, the ratio of their volumes will be . Cancelling out the equal terms we find the ratio as $2:3$.