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:

`V=(4)/(3) \pi r^3`
r - the radius

The volume of a cone:

`V=(1)/(3) \pi r^2 h`
r - the radius
h - the height

Each figure has a radius of 3 inches, the figures have the same volume.

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

The height of the cone is 12 inches.