The first theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to product of the arc length s of C and the distance d1 traveled by its centroid. For example, the surface area of the torus with minor radius r and major radius R is ...

See also:

Pappus's centroid theorem, Pappus's centroid theorem - The first theorem, Pappus's centroid theorem - The second theorem

Read more here: » Pappus's centroid theorem: Encyclopedia II - Pappus's centroid theorem - The first theorem