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?
Show your work.
Plz help

Answer 1

Answer: 4 in

Explanation:

The volume of the cylinder is

`V=(\pi)(2^(2))(3)=12\pi`

If we let the height of the cone h, the volume of the cone is

`V=(1)/(3)(\pi)(3^(2))(h)=3\pi h`

Setting these volumes equal,

`12\pi=3\pi h\\\\12=3h\\\\h=\boxed{4 \text{ in}}`