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

Data from Theorem of Pappus

The solid formed by revolving the region bounded by the graphs of y = x, y = 4, and x = 0 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.)