Chapter 15.3, Problem 27E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

**27.** Inside both the cylinder *x*^{2} + *y*^{2} = 4 and the ellipsoid 4*x*^{2} + 4*y*^{2} + *z*^{2} = 64

To determine

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

Explanation

**Given:**

The region *D* lies inside the cylinders

**Formula used:**

If
*R* given by

If

**Calculation:**

Obtain the value for *z* from the ellipsoid.

And, the value of *r* varies from 0 to 2 and the value of

Substitute

Integrate the function with respect to *r* and

Let

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