   Chapter 2.9, Problem 32E

Chapter
Section
Textbook Problem

# The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm.(a) Use differentials to estimate the maximum error in the calculated area of the disk.(b) What is the relative error? What is the percentage error?

To determine

(a)

To estimate:

The maximum error in the calculated area of disk.

Explanation

1) Formula:

A= πr2 Where, r be the radius of a circular disk

If the error in the measured value of r is denoted by dr = ∆r, then the corresponding maximum possible error in the calculated value of A is ∆A, which can be approximated by the differential,

dA=2π r dr

A   2πr r

Relative error is calculated by dividing the maxi

To determine

b)

To find:

The relative error and the percentage error.

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