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:
$V=\frac{4}{3} \pi r^3$
r - the radius

The volume of a cone:
$V=\frac{1}{3} \pi r^2 h$
r - the radius
h - the height

Each figure has a radius of 3 inches, the figures have the same volume.
$\frac{4}{3} \pi \times 3^3=\frac{1}{3} \pi \times 3^2 \times h \\ \frac{4}{3} \pi \times 27 = \frac{1}{3} \pi \times 9 \times h \ \ \ \ \ \ \ \ |\div \pi \\ \frac{4}{3} \times 27=\frac{1}{3} \times 9 \times h \ \ \ \ \ \ \ \ \ \ \ \ |\times 3 \\ 4 \times 27=9 \times h \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\div 9 \\ 4 \times 3=h \\ h=12$

The height of the cone is 12 inches.