Question

A cone, a hemisphere and a cylinder have the same base and same height. Calculate the ratio of their volumes.

Answer 1

Let the base radii of them be $r$ and height $h.$

Then ratio of volumes
cone : hemisphere : cylinder
$=\frac{1}{3}\pi r^{2}h:\frac{2}{3}\pi r^3:\pi r^{2}h$ [but h = r]

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

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

$=\frac{1}{3}:\frac{2}{3}:1$

$=1:2:3$