University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.11 - Linearization and Differentials - Exercises - Page 199: 51


a) $0.08\pi\ m^2$ b) 2%

Work Step by Step

Area of a circle: $A=\pi r^2$ differentiating the above: $dA=2\pi r dr$ radius r =2.00m change in radius(dr)= final radius - initial radius = $2.02-2.00=.02m$ so $dA=2\pi\ 2\times.02=0.08\pi$ $%change in Area = \frac{dA}{\pi r^2}\times100=\frac{0.08\times100}{\pi\times2^2}=2%$
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