Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises: 74

Answer

a) $4849.05$ cm$^{3}$ b) $r = 8.89$ cm

Work Step by Step

a) $V = \frac{4}{3}\pi r^{3}$ $V = \frac{4}{3}\pi (10.5)^{3}$ $= \frac{4}{3}\pi (1157.625)$ $= \frac{4\pi (1157.625)}{3}$ by GDC / calculator $= \frac{4630.5\pi}{3}$ $= 4849.05$ cm$^{3}$ b) $2943 = \frac{4}{3}\pi r^{3}$ $2943 = \frac{4\pi r^{3}}{3}$ $8829 = 4\pi r^{3}$ $2207.25 = \pi r^{3}$ $\frac{2207.25}{\pi} = r^{3}$ $r = (\frac{2207.25}{\pi})^{\frac{1}{3}}$ $r = 8.89$ cm
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