(a)
To find: The formula for the approximate volume of the thin cylindrical shell with height h, inner radius r and thickness
(a)
Answer to Problem 31E
The formula for approximate value of the cylindrical shell is
Explanation of Solution
Calculation:
The volume of the cylindrical shell with r is the radius and h is height is
Here, the value h is constant and the value r is changeable variable.
The differential is
The derivative of the function
Substitute
The thickness of the cylindrical shell is
Therefore, the formula for approximate value of the cylindrical shell is
(b)
To find: The error involved in using the formula from part (a).
(b)
Answer to Problem 31E
The error is
Explanation of Solution
Calculation:
The volume of the cylindrical shell with r is the radius and h is height is
The volume of the cylindrical shell with radius is
The volume of the thin cylindrical shell with height h, inner radius r and thickness
The error
Therefore, the error is
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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