Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.8 Related Rates - 2.8 Exercises - Page 185: 6


$80424.772$ $mm^3/s$

Work Step by Step

Given information: $\displaystyle \frac{dr}{dt} = 40 $ mm/s, $d = 80$mm What we're trying to find: Change in volume with respect to time ($\displaystyle \frac{dV}{dt}$) Diameter = 2$\cdot$radius, d = 2r, therefore $80 = 2r \rightarrow r=40$ mm --- Volume of a sphere: $\displaystyle V = \frac{4}{3}πr^3$ Implicitly differentiate with respect to time: $\displaystyle \frac{dV}{dt} = 4πr^2\cdot\frac{dr}{dt}$ Now we can plug in our givens: $\displaystyle \frac{dV}{dt} = 4π(40)^2(4)$ $\displaystyle \frac{dV}{dt} = 80424.772$ $mm^3/s$
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.