Surface Area of Frustums

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 isand 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 giveandsubstituting into (2) gives

Add on the top and bottom to give


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