Chapter 15.8, Problem 28E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**28.** Find the average distance from a point in a ball of radius *a* to its center.

To determine

**To find:** The average distance of the given point from the center by using spherical coordinates.

Explanation

**Given:**

The region *B* is the ball of radius *a*.

**Formula used:**

The average distance of the given pointis,
*B.*

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

By the given conditions, it is observed that
*a*,
*a.* So, the volume of the region is given by

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