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: 14


$0.533\pi\, m^{3}/min$

Work Step by Step

$r=2\,m, h=3\,m$$\implies\frac{r}{h}=\frac{2}{3}\implies r=\frac{2}{3}h$ $V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (\frac{2}{3}h)^{2}h=\frac{4\pi}{27}h^{3}$ $\frac{dV}{dt}=\frac{dV}{dh}\times\frac{dh}{dt}$$=\frac{4\pi}{27}\times3h^{2}\times\frac{dh}{dt}=\frac{12\pi}{27}\times h^{2}\times\frac{dh}{dt}$ When $\frac{dh}{dt}= 0.3\,m/min$ and $h=2\,m$, $\frac{dV}{dt}= \frac{12\pi}{27}\times(2\,m)^{2}\times0.3\,m/min$ $\approx0.533\pi\,m^{3}/min$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.