Chapter 14.4, Problem 49E

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11th Edition

Ron Larson + 1 other

ISBN: 9781337275347

Textbook Problem

Proof Prove the following 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*. 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
*A* is the area of *R*.

To determine

**To Prove:** The Second Theorem of Pappus: Assume *R*.

Explanation

**Given:**

*R*.

**Proof:**

Using the data given in the question, draw the figure with reference to *xy-coordinate* with the orientations that are shown below.

The volume of this solid can be written as:

Now, solve the double integral to get:

Now, multiply and divide *V* by

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