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Suppose a curve C in the plane is rotated around an axis that does not intersect C to form a surface of revolution. Then the area of the surface generated is sd, where s is the length of C, and d is the circular distance traveled by the centroid of C.
Now "centroid" of a curve is not a trivial matter in general, but there are some easy cases: The centroid of a circle is its center, and the centroid of a line segment is its midpoint. In this module you encountered at least one case of Pappus's Theorem, and possibly others. Identify the case(s), and explain the connection(s).
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