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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

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 Δ r .

(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 ∆V = Difference between the volume of the outer cylinder with radius r+ r and the volume of the inner cylinder with radius r.

Exact volume of the shell ∆V = π  r+ r2 h-    π r2h  ……………………. (1)

2) Given:

Height h, inner radius r and thickness ▵r for the thin cylindrical shell

3) Calculation:

Differentiate V= π r2h  with respect to r

To determine

(b)

To find:

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

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