Calculus (3rd Edition)

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

Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 298: 35


$128 \pi \ \ \mathrm{cm}^{3}/\mathrm{s}$

Work Step by Step

The flow rate is given by $$ 2 \pi \int_{0}^{R} r v(r) d r=2 \pi \int_{0}^{4} r\left(16-r^{2}\right) d r\\ =\left.2 \pi\left(8 r^{2}-\frac{1}{4} r^{4}\right)\right|_{0} ^{4}=128 \pi \ \ \mathrm{cm}^{3}/\mathrm{s} $$
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