Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.9 Related Rates - Exercises - Page 159: 6


$432000\pi\, cm^{3}/min $

Work Step by Step

$\frac{dV}{dt}=\frac{dV}{dr}\times\frac{dr}{dt}=\frac{d}{dr}(\frac{4}{3}\pi r^{3})\times30\,cm/min $ $=4\pi r^{2}\times30\,cm/min $ As $\frac{dr}{dt}=30\,cm/min $ and $ r=0$ at $ t=0$, the radius at t=2 min is $2\,min\times30\,cm/min=60\,cm $ Then, $\frac{dV}{dt}|_{t=2\,min}=4\pi(60\,cm)^{2}\times30\,cm/min=432000\pi\, cm^{3}/min $
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