Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.9 Related Rates - Exercises - Page 159: 4


$2\sqrt {3}\,cm/s $

Work Step by Step

Let the diagonal of the cube be $ r $ and its edge be $ a $. We are given that $\frac{da}{dt}=2\,cm/s $ The length of the diagonal of a cube with edge length equal to $ a $ is $\sqrt {3}a $. That is, $ r=\sqrt {3}a $ $\frac{dr}{dt}=\frac{dr}{da}\times\frac{da}{dt}=\frac{d}{da}(\sqrt {3}a)\times2\,cm/s $ $=2\sqrt {3}\,cm/s $
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