Chapter 15.8, Problem 31E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**31.** (a) Find the centroid of the solid in Example 4. (Assume constant density *K*.)

(b) Find the moment of inertia about the z-axis for this solid.

(a)

To determine

The centroid of the solid in example 4 by using spherical coordinates.

Explanation

**Formula used:**

If *E* given by

If *z* then,

The spherical coordinates

**Calculation:**

From example 4, it is known that

Integrate with respect to

(b)

To determine

The moment of inertia about the *z* axis.

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