Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.6 Exercises - Page 153: 14


a) 0.0707 cm/min b) 0.0177 cm/min

Work Step by Step

The volume of a sphere is $\frac{4}{3} \pi r^3 $ The change in volume is given by $\frac {dV}{dt} = (4/3) (3) \pi r^2 = 4 \pi r^2 \frac{dr}{dt} $ We are told the volume is changing at a rate of + 800 $cm^3$ (positive since inflated) $800 = 4 \pi r^2 {dr}{dt} $ a) when the radius is 30cm, we solve for dr/dt $\frac {dr}{dt} = 0.0707 cm/min $ b) when the radius is 60cm, we solve for dr/dt $\frac {dr}{dt} = 0.0177 cm/min $
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