## Surface Area of Frustums

A frustum is that past of a pyramid or cone that lines between twoparallel planes cutting it. If one of the planes is the base and theother is horizontal then the result is the shape shown below right(for a cone).

The smaller cone top right and the original cone left are similarshapes, so(1)

The curved surface area of the original cone isandthe curved surface area of the smaller cone is

Thedifference between these two is the curved surface area of thefrustum.

(abovebottom right), (2)

Rearranging (1) to giveandsubstituting into (2) gives

Add on the top and bottom to give

Ifthenandsoand