Question

A sphere and a cone have the same volume. each figure has a radius of 3 inches.

what is the height of the cone?

Answer 1

The volume of a sphere -
`(4)/(3) \pi r^3`
The volume of a cone -
`(1)/(3) \pi r^2 h`
r - radius, h - height

The sphere and the cone have the same volume and the radius is 3 inches.

`(4)/(3) \pi * 3^3=(1)/(3) \pi * 3^2 * h \ \ \ |/ \pi \\ (4)/(3) * 27=(1)/(3) * 9 * h \\ 36=3h \ \ \ |/ 3 \\ h=12`

The height of the cone is 12 inches.