Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.4 Tangent Planes and Linear Approximations - 14.4 Exercises - Page 975: 34

Answer

$8.792 cm^3$

Work Step by Step

Volume , $V=\pi r^2 h$ Write the differential form such as: $dV=\dfrac{\partial V}{\partial r} \times dr + \dfrac{\partial V}{\partial h} \times dh$ This gives: $dV=[ 2 \pi r h] dr+[ \pi r^2] dh$ Now, need to plug the given data. $dV=[ 2 \pi \times 2 \times 10] \times (0.05)+4 \times (0.2)$ Thus, we get $dV=\dfrac{14 \pi}{5} cm^3$ or, $dV=8.792 cm^3$
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