Question

A cylinder, $a$cone and a hemisphere are of base and have the same height what is the ratio in their volume?

Answer 1

Let $r$ and $h$ be the radius of base and height of the cylinder, cone and hemisphere.

We know that, Height of hemisphere$=$Radius of the hemisphere.

$\therefore h=r$

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

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

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

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

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

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

$=3:1:2$

Thus, the ratio of their volumes is $=3:1:2$