Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set - Page 454: 63

Answer

$\text{ approximately } 14,657,414 \text{ square miles}$

Work Step by Step

Substituting $r=1080$ in the given formula, $ r=\sqrt{\dfrac{A}{4\pi}} ,$ results to \begin{array}{l}\require{cancel} 1080=\sqrt{\dfrac{A}{4\pi}} .\end{array} Squaring both sides and using the properties of equality, the equation above is equivalent to \begin{array}{l}\require{cancel} (1080)^2=\left(\sqrt{\dfrac{A}{4\pi}}\right)^2 \\ 1166400=\dfrac{A}{4\pi} \\ 4\pi\cdot1166400=\dfrac{A}{4\pi}\cdot4\pi \\ 14,657,414=A .\end{array} Hence, the surface area of the moon, $A,$ is $ \text{ approximately } 14,657,414 \text{ square miles} .$
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