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 - Page 250: 35

Answer

The rate at which the minute hand sweeps out area is $\frac{\pi~r^2}{3600}~cm^2/s$

Work Step by Step

Let $r$ be the length of the minute hand. Then the total area swept out by the minute hand is $A = \pi~r^2$ The minute hand sweeps out this area in one hour, which is 3600 seconds. The rate at which the minute hand sweeps out area is: $\frac{dA}{dt} = \frac{\pi~r^2}{3600}~cm^2/s$
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