A cone and a hemisphere have equal bases and equal volumes. Find the ratio in their heights.

 Given:

A cone and a hemisphere have equal bases and equal volumes. 

To do:

We have to find the ratio in their heights.

Solution:

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

This implies,

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

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

Their volumes are equal.

Therefore,

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

$\frac{1}{3} h=\frac{2}{3} r$

$\frac{h}{r}=\frac{2}{3} \times \frac{3}{1}$

$\frac{h}{r}=\frac{2}{1}$

The ratio in their heights is $2:1$.

Tutorialspoint

e

Updated on: 10-Oct-2022

31 Views

Kickstart Your Career

Get certified by completing the course

Get Started