Chapter 15.7, Problem 28E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical coordinates.

28. Find the mass of a ball *B* given by *x*^{2} + *y*^{2} + z^{2}
*a*^{2} if the density at any point is proportional to its distance from the *z*-axis.

To determine

**To find:** The mass of the given ball.

Explanation

**Given:**

The ball *B* is

The density function is proportional to the distance from the *z-*axis that is

**Calculation:**

The mass of the given solid *S* is,
*r* varies from 0 to *a.* To find the limits of *z* solve the given equations.

Therefore, the mass of the given solid is given by,

Integrate with respect to *z* and apply the limit of it.

Separate the integrals, and integrate with respect to

Integrate with respect to *r* and apply the limit of it

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