Chapter 15.8, Problem 36E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use cylindrical or spherical coordinates, whichever seems more appropriate.

**36.** Find the volume of the smaller wedge cut from a sphere of radius *a* by two planes that intersect along a diameter at an angle of π/6.

To determine

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

Explanation

**Given:**

The region *B* is a small wedge cut from a sphere of radius *a* by two planes that intersect along a diameter at an angle of

**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 is given, it is more appropriate to use the spherical coordinates. By the given conditions, it is observed that
*a*,

Integrate with respect to

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