Question

A cylinder, a hemisphere, and a cone have an equal base diameter and have the same height. Prove that their volume are in the ratio $3:2:1$.

Answer 1

For cylinder,

$Radius=Height=r$

For hemisphere,

$Radius=r$

For cone,

$Radius=Height=r$

Volume of cylinder = $\pi r^{2}h=\pi r^3$

Volume of hemisphere = $\frac{2}{3}\pi r^3$

Volume of Cone = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^3$

Hence, ratio of Volumes is:

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

$=3:2:1$