A frustum is the part of a pyramid or cone between two parallel planes cutting it. If one of the planes is the base and the other is horizontal then the result is the shape shown (for a cone).
The smaller cone top right and the original left are similar, so
(1)
The curved surface area of the original cone is
and the curved surface area of the smaller is
The difference between these is the curved surface area of the frustum.
(above bottom right), (2)
Rearranging (1) to give
andsubstituting into (2) gives
Add on the top and bottom to give
If
then
and
so
and
