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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.
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