Chapter 5.2, Problem 69E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A hole of radius *r* is bored through the middle of a cylinder of radius

To determine

**To find:**

Integral for the volume of cut out

Explanation

**1) Concept:**

i) Solid of Revolution:

Volume of solid revolution revolving a region around a line is given by

In case of the disk method, the radius is found in terms of x or y and use

In case of the washer method, find the inner and outer radius and compute the area of washer by subtracting the area of inner disk from outer disk, use

ii) Integrals of Symmetric functions:

Suppose

a) If

b) If

**2) Calculation:**

Now from the front side, the circle appears to be in a y-z plane,

Therefore, equation of circle is

From the top side, the hole lies on a x-y plane,

Therefore, equation of circle is

From the front side, the diagram will appear as shown below:

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