Chapter 15.8, Problem 30E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**30.** Find the volume of the solid that lies within the sphere *x*^{2} + *y*^{2} + *z*^{2} = 4, above the xy-plane, and below the cone *z* =

To determine

**To find:** The volume of the given region by using spherical coordinates.

Explanation

**Given:**

The region *B* lies within the sphere
*xy-*plane and below the cone

**Formula used:**

The volume of the given region *B* is,

If
*E* given by

If
*z* then,

The spherical coordinates

**Calculation:**

By the given conditions, it is observed that

So,

Integrate with respect to

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