Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.9 - Related Rates - 3.9 Exercises: 2

Answer

a. $\frac{dA}{dt} = 2\pi r \times \frac{dr}{dt}$ b. $\frac{dA}{dt} = 60\pi m^2/s$

Work Step by Step

a. $A(r) = \pi r^2$ $\frac{dA}{dt} = \frac{d(\pi r^2)}{dt}$ $\frac{dA}{dt} = 2\pi r \times \frac{dr}{dt}$ b.$\frac{dA}{dt} = 2\pi r \times \frac{dr}{dt}$ $\frac{dA}{dt} = 2\pi (30) \times (1)$ $\frac{dA}{dt} = 60\pi m^2/s$
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