Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises: 26

Answer

A(r)=4$\pi$$r^{2}$+4$\pi$r+$\frac{4}{3}$$\pi$

Work Step by Step

Let the amount of air required as a function of the original radius of the balloon be A(r). A(r) = V(r+1)-V(r) = $\frac{4}{3}$$\pi$$(r+1)^{3}$-$\frac{4}{3}$$\pi$$r^{3}$ = $\frac{4}{3}$$\pi$[$(r+1)^{3}$-$r^{3}$] = $\frac{4}{3}$$\pi$[$r^{3}$+3$r^{2}$+3r+1-$r^{3}$] = $\frac{4}{3}$$\pi$[3$r^{2}$+3r+1] = 4$\pi$$r^{2}$+4$\pi$r+$\frac{4}{3}$$\pi$
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