Chapter 15.8, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical or spherical coordinates, whichever seems more appropriate.

**35.** Find the volume and centroid of the solid *E* that lies above the cone z =
*x*^{2} + *y*^{2} + *z*^{2} = 1.

To determine

**To find:** The volume and centroid of the given region by using spherical or cylindrical coordinates.

Explanation

**Given:**

The region *B* lies above the cone

**Formula used:**

The volume of the given region *B* is,

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

Since the equation of the sphere and cone is given, it is more appropriate to use spherical coordinates. By the given conditions, it is observed that

So,

Integrate with respect to

Use (2) to integrate and apply the limit values

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