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

ANSWER

$h= 4in.$

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,

$v = \pi \times {2}^{2} \times 3$

$v =12 \pi$

The volume of a cone is given by

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

The cone has a radius of 3 inches:

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

$v=3 \pi h$

The two volumes are the same:

This implies that,

$3 \pi h = 12\pi$

Divide both sides by 3π

$h= 4in$