In Exercises use the Theorem of Pappus to find the volume of the solid of revolution.

Data from Theorem of Pappus

The torus formed by revolving the circle

about the x-axis

Transcribed Image Text:

THEOREM 7.1 The Theorem of Pappus Let R be a region in a plane and let L be a line in the same plane such that L does not intersect the interior of R, as shown in Figure 7.63. If r is the distance between the centroid of R and the line, then the volume V of the solid of revolution formed by revolving R about the line is V = 2wrA where A is the area of R. (Note that 27r is the distance traveled by the centroid as the region is revolved about the line.)