College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Focus on Modeling - Modeling with Functions - Problems - Page 276: 8


$S(V)=6V^{\frac{2}{3}}$, $V>0$

Work Step by Step

We know that the volume of a cube of side $x$ is: $V=x^3$ And the surface area is: $S=6x^2$ We solve for $x$ in the volume formula: $V=x^3$ $x=\sqrt[3]{V}=V^{1/3}$ And plug into the surface area formula: $S=6x^2$ $S=6(V^{\frac{1}{3}})^2=6V^{\frac{2}{3}}$ We restrict $V>0$.
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