Chapter 15.7, Problem 13E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A cylindrical shell is 20 cm long, with inner radius 6 cm and outer radius 7 cm. Write inequalities that describe the shell in an appropriate coordinate system. Explain how you have positioned the coordinate system with respect to the shell.

To determine

**To write:** The description of the given shell in an appropriate coordinates system; explain how the coordinate system has been positioned with respect to the shell.

Explanation

**Given:**

The shell is 20 cm long, inner radius 6 cm and outer radius 7 cm.

Since the inner and outer radius of the shell is given, it is easy to use the cylindrical coordinates.

Place the center of the cylinder in the origin. Every horizontal cut of the cylinder is the circle in the *xy*-plane. Therefore,

Moreover, from the given conditions, it is observed that *r* varies from 6 to 7.

Since the length of the shell is 20 cm, the height of the cylinder is 20 cm. And the shell is placed at the origin. Therefore, *z* varies from

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