Question

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

Answer 1

The volume of a sphere - $\frac{4}{3} \pi r^3$
The volume of a cone - $\frac{1}{3} \pi r^2 h$
r - radius, h - height

The sphere and the cone have the same volume and the radius is 3 inches.
$\frac{4}{3} \pi \times 3^3=\frac{1}{3} \pi \times 3^2 \times h \ \ \ |\div \pi \\ \frac{4}{3} \times 27=\frac{1}{3} \times 9 \times h \\ 36=3h \ \ \ |\div 3 \\ h=12$

The height of the cone is 12 inches.