Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.8 - Related Rates - Exercises 3.8 - Page 161: 2


$\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$

Work Step by Step

Surface area of a sphere (S) can be found as: S = $4\pi r^2$ On differentiation , we get: $\dfrac{dS}{dt}$ = $\dfrac{d (4\pi r^2)}{dt}$ or, $\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$ Hence, $\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$
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