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: 5


$27000\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 $ $=\frac{4}{3}\times3\times\pi r^{2}\times 30\,cm/min $ $=120\pi r^{2}\, cm/min $ $=120\pi(15\,cm)^{2}\,cm/min $ $=27000\pi\,cm^{3}/min $
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