A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio $1:2:3$.

Volume of cone $=(1-3)\pi r^{2}h$

Volume of hemisphere $=\left(2/3\right)\pi r^3$

Volume of cylinder $=\pi r^{2}h$

Given that cone, hemisphere and cylinder have

equal base and same height

That is $r=h$

Volume of cone : Volume of hemisphere : Volume of cylinder $=$

$=\frac{1}{3}\pi r^{2}h\therefore 2/3\pi r^3:\pi r^{2}h$

$=1/3:2/3:1$

$=1:2:3$