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A surface of revolution is formed by the rotation of a planar curve C about an axis in the plane of the curve and not cutting the curve. The Pappus--Guldinus theorem says that:
When C is a circle, the surface obtained is a circular torus or torus of revolution (Figure 1). Let r be the radius of the revolving circle and let R be the distance from its center to the axis of rotation. The area of the torus is 4Rr, and its volume is 2Rr.
Figure 1: A torus of revolution.
Wed Oct 4 16:41:25 PDT 1995
This document is excerpted from the 30th Edition of the CRC Standard Mathematical Tables and Formulas (CRC Press). Unauthorized duplication is forbidden.