Chapter 15.3, Problem 22E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use polar coordinates to find the volume of the given solid.

**22.** Inside the sphere *x*^{2} + *y*^{2} + *z*^{2} = 16 and outside the cylinder *x*^{2} + *y*^{2} = 4

To determine

**To find:** The volume of the given solid by using polar coordinates.

Explanation

**Given:**

The region *D* lies inside the sphere and outside the cylinder.

The spherical surface is,

The cylindrical region is,Â

**Formula used:**

If
*R* given by

If

**Calculation:**

From the given region *D*, it is observed that the sphere and the cylinder intersects the *xy-*plane. So, the value of *r* varies from 2 to 4 and the value of

Substitute

Integrate the function with respect to *r* and

Let

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