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: 57


Greatest % error in height: $\frac{1}{3}$% of h

Work Step by Step

We need to find % error change in height: $\frac{dh}{h}$ % error change in volume = 1% % error change=$\frac{change\ in\ dimension}{original\ dimension}$ $V=\pi h^3$ $dV=3\pi h^2 dh$ % error in volume=$\frac{dV}{V}=\frac{3\pi h^2dh}{\pi h^3}=3 \frac{dh}{h}$ $\frac{dh}{h}=\frac{1}{3}$%
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