Chapter 15.8, Problem 33E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**33.** (a) Find the centroid of a solid homogeneous hemisphere of radius *a*.

(b) Find the moment of inertia of the in part (a) about a diameter of its base.

(a)

To determine

**To find:** The centroid of the solid in example 4 by using spherical coordinates.

Explanation

**Given:**

The solid is the hemisphere of radius *a.*

**Formula used:**

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

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

Use the equation (2) to separate the integrals and integrate it.

=

Thus, the mass of the given solid is

(b)

To determine

**To find:** The moment of inertia about the diameter of its base for the region in part (a).

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