Chapter 15.8, Problem 29E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use spherical coordinates.

**29.** (a) Find the volume of the solid that lies above the cone *ϕ* = π/3 and below the sphere *ρ* = 4 cos *ϕ*.

(b) Find the centroid of the solid in part (a).

(a)

To determine

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

By the given conditions, it is observed that

Integrate with respect to

(b)

To determine

**To find:** The centroid of the solid in part (a).

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