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: 103

Answer

$\color{blue}{A\approx 114.0 \space cm^2}$

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. Convert the angle to radians to obtain: $81^o \\=81^o\cdot \dfrac{\pi}{180^o} \\=\dfrac{9\pi}{20}$ Substitute the given values of the radius and $\theta$ to obtain: $A=\frac{1}{2}r^2\theta \\A=\frac{1}{2}(12.7^2)(\frac{9\pi}{20}) \\A=114.0091828 \\\color{blue}{A\approx 114.0 \space cm^2}$
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