Chapter 2.9, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

(a) Use differentials to find a formula for the approximate volume of a thin cylindrical shell with height *h,* inner radius *r,* and thickness

(b) What is the error involved in using the formula from part (a)?

To determine

**(a)**

**To find:**

A formula for the approximate volume of a thin cylindrical shell using differentials.

Explanation

**1) Formula:**

The exact volume of the shell âˆ†V = Difference between the volume of the outer cylinder with radius

Exact volume of the shell âˆ†V

**2) Given:**

Height h, inner radius r and thickness â–µr for the thin cylindrical shell

3) **Calculation:**

Differentiate

To determine

**(b)**

**To find:**

The error involved in the formula from part (a).

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