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