Chapter 15.8, Problem 34E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**34.** Find the mass and center of mass of a solid hemisphere of radius *a* if the density at any point is proportional to its distance from the base.

To determine

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

Explanation

**Given:**

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

The density function is proportional to its distance from the base say *Kz.*

**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. For that, substitute

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