Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 6 - Applications of the Integral - 6.5 Work and Energy - Exercises - Page 317: 11


$$105840 \mathrm{J}$$

Work Step by Step

The volume of one layer is 4 $\Delta y \mathrm{m}^{3}$ and so the weight of one layer is $23520 \Delta y$ N. Thus, the work done against gravity to build the tower is \begin{align*} W&=\int_{0}^{3} 23520 y d y\\ &=\left.11760 y^{2}\right|_{0} ^{3}\\ &=105840 \mathrm{J} \end{align*}
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