Precalculus (6th Edition)

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

Chapter 6 - The Circular Functions and Their Graphs - 6.1 Radian Measures - 6.1 Exercises: 108

Answer

$\color{blue}{r \approx 17 \text{ m}}$

Work Step by Step

RECALL: The area of a sector $(A)$ intercepted by a central angle $\theta$ on a circle whose radius is $r$ is given by the formula: $A = \frac{1}{2}r^2\theta$, where $\theta$ is in radian measure. Substitute the given values of the the central angle and the area of the sector to obtain: $A=\frac{1}{2}r^2\theta \\64=\frac{1}{2}(r)(\frac{\pi}{6}) \\64=r(\frac{\pi}{12}) \\\frac{\pi}{12} \cdot 64=r \\16.75516082 =r \\\color{blue}{r \approx 17 \text{ m}}$
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