Chapter 15.3, Problem 25E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

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

**25.** Above the cone
*x*^{2} + *y*^{2} + *z*^{2} *=* 1

To determine

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

Explanation

**Given:**

The region *D* lies above the cone

**Formula used:**

If
*R* given by

If

**Calculation:**

Substitute

So, the value of *r* varies from 0 to

Substitute

Integrate the function with respect to *r* and

Let

Then,

Compute the volume as follows

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