The volume of a sphere:
[tex]V=\frac{4}{3} \pi r^3[/tex]
r - the radius
The volume of a cone:
[tex]V=\frac{1}{3} \pi r^2 h[/tex]
r - the radius
h - the height
Each figure has a radius of 3 inches, the figures have the same volume.
[tex]\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
[/tex]
The height of the cone is 12 inches.
