Chapter 5.3, Problem 45E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Use cylindrical shells to find the volume of the solid.

A sphere of radius *r*

To determine

**To find:**

The volume of the sphere of the radius

Explanation

**1) Concept:**

i. If

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

where,Â

**2) Given:**

The radius of the sphere is

**3) Calculation:**

A sphere is obtained by rotating the region under the curve

Hus we have

Let the given region rotate about the

Using the shell method, find the typical approximating shell with the radius

The figure gives top half of height of a typical shell. By symmetry therefore, the circumference is

So, the total volume is

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