Pappus's centroid theorem

Sajun.org

'''Pappus's centroid theorem''' states that the area of a surface of revolution generated by rotating a plane curve <math>C</math> about an axis external to <math>C</math> and on the same plane is equal to the length of <math>C</math> times the distance traveled by its centroid. For example, the surface area of the torus with minor radius <math>r</math> and major radius <math>R</math> is :<math>A = (2\pi r)(2\pi R) = 4\pi^2 R r</math>. It is attributed to Pappus of Alexandria.