Chapter 14.7, Problem 48E

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6th Edition

Ron Larson + 1 other

ISBN: 9781285774770

Textbook Problem

HOW DO YOU SEE IT? The solid is bounded below by the upper nappe of a cone and above by a sphere (see figure). Would it be easier to use cylindrical coordinates or spherical coordinates to find the volume of the solid? Explain.

To determine

**To Calculate:** Whether it would be easier to use cylindrical coordinates or spherical coordinates to calculate volume of the given solid bounded below by the upper nappe of a cone

Explanation

**Given:**

The figure:

Refer to figure in question.

The solid is bounded below by the upper nappe of a cone

**Formula used:**

Volume of a solid in cylindrical coordinates is,

And volume of a solid in spherical coordinates is,

**Calculation:**

It is clear from the figure that

Consider the general equation of sphere that is

Where

Now the cone

Take square root on both the sides,

It is known that in spherical coordinate

Where

Substitute the value of

Thus, bounds of

For sphere angle

Hence, volume of provided solid is,

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