Question

A right-circular cone is inscribed in a sphere having a fixed radius of 10 in.

Express the volume of the cone as a function of its radius.

Answer 1

By Pythagorean theorem we have 10²=R²+(H-10)² (see the picture).

Therefore, H = 10+(100-R²)^1/2; and V = $\pi$ (10+(100-R²)^1/2)R²/3.