Chapter 5.3, Problem 1E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Let *S* be the solid obtained by rotating the region shown in the figure about the *y*-axis. Explain why it is awkward to use slicing to find the volume *V* of *S*. Sketch a typical approximating shell. What are its circumference and height? Use shells to find *V*.

To determine

**To find:**

The volume of the solid obtained by rotating the region shown in the figure about the

Explanation

**1) Concept:**

i. If

ii. By the shell method, the volume of the solid by rotating the region under the curve

Where

**2) Given:**

The region bounded by

**3) Calculation:**

As the region is bounded by

let us consider the problem of finding the volume by the washer method.

If we slice perpendicular to

To compute the inner radius and the outer radius of the washer, we would have to solve the cubic equation.

that is, to find the functions

Using the shell method, the typical approximating shell with radius

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