Question

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

Answer 1

volume of cone is equal to volume of hemisphere
1/3pi r2h = 2/3pi r2h
1/3h = 2/3h
1h = 2/3 * 3 h
therefore ratio of there heights is
1:2

Answer 2

Answer:

$Ratio of heights = \frac{h}{r} = \frac{2}{1}$

Step-by-step explanation:

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

Let base radius of the cone =base radius of the hemisphere = r

Height of the cone = h

_________________________

We know that,

$\boxed {volume\: of \:cone \: \\= \frac{1}{3}\pi r^{2} h}$

$\boxed {volume \:of \:the \:hemisphere\\ = \frac{2}{3}\pi r^{3}}$

__________________________

According to the problem given,

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

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

After cancellation, we get

$\implies h = 2r$

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

Therefore,

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

•••♪