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: 3

Answer

Area is increasing at $48 \frac{cm^{2}}{s}$

Work Step by Step

The area of the square is $A(x) = x^{2}$ $\frac{dA}{dt} = \frac{d(x^{2})}{dt}$ $\frac{dA}{dt} = 2x \times \frac{dx}{dt}$ $\frac{dA}{dt} = 2x \times 6$ Using the radius of the area $x = 4$ $\frac{dA}{dt} = 2(4) \times 6$ $\frac{dA}{dt} = 8 \times 6$ $\frac{dA}{dt} = 48 \frac{cm^{2}}{s}$
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