Let r and h be the radius and the height (altitude) of the cone respectively.
Then, the volume (V) of the cone is given as:
The surface area (S) of the cone is given by, S = πrl (where l is the slant height)
Thus, it can be easily verified that when 
∴ By second derivative test, the surface area of the cone is the least when 
Hence, for a given volume, the right circular cone of the least curved surface has an altitude equal to √2 times the radius of the base.
