Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - Chapter 2 Test Prep - Review Exercises - Page 300: 129

Answer

$\frac{4}{3}\pi (r+3)^3-\frac{4}{3}\pi r^3$

Work Step by Step

Step 1. Given $V(r)=\frac{4}{3}\pi r^3$, for $r\to r+3$, we have $V(r+3)=\frac{4}{3}\pi (r+3)^3$ Step 2. The volume gain is $V'(r)=\Delta V=V(r+3)-V(r)=\frac{4}{3}\pi (r+3)^3-\frac{4}{3}\pi r^3$
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