Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.4 Rates of Change - Exercises - Page 129: 7


$V' = 3\pi r^2$

Work Step by Step

First, we look at the equation for the volume of a cylinder: $V = \pi r^2 h$ We are given that the height is equal to the radius, so we can simply the formula to be: $V = \pi r^3$ Now, for the rate of change, we need to find the derivative of the function with respect to the radius: $V' = 3\pi r^2$
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