Question

A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches. What is the height of the cone ? I need this ASAP hurry!!!!

Answer 1

`h= 4in.`

Step-by-step explanation

The volume of a cylinder is calculated using the formula;

`v = \pi \: {r}^(2) h`

It was given that, the cylinder has a radius of 2 inches and a height of 3 inches.

This implies that,

`v = \pi * {2}^(2) * 3`

`v =12 \pi`

The volume of a cone is given by

`v = (1)/(3) * \pi {r}^(2) h`

The cone has a radius of 3 inches:

`v=(1)/(3) * \pi * {3}^(2) h`

`v=3 \pi h`

The two volumes are the same:

This implies that,

`3 \pi h = 12\pi`

Divide both sides by 3π

`h= 4in`