Chapter 15.8, Problem 32E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**32.** Let *H* be a solid hemisphere of radius *a* whose density at any point is proportional to its distance from the center of the base.

(a) Find the mass of *H*.

(b) Find the center of mass of *H*.

(c) Find the moment of inertia of *H* about its axis.

(a)

To determine

**To find:** The mass of the given solid by using spherical coordinates.

Explanation

**Formula used:**

If
*E* given by

If
*z* then,

The spherical coordinates

**Given:**

The solid *H* is the hemisphere of radius *a.*

The density function is proportional to its distance from the center of the base say *K.*

**Calculation:**

From the given condition, it is observed that
*a*,

(b)

To determine

**To find:** The centroid of the given region *H.*

(c)

To determine

**To find:** The moment of inertia about the *z* axis.

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