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: 106

Answer

$\color{blue}{A\approx 19,085.2 \space km^2}$

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: $270^o \\=270^o\cdot \dfrac{\pi}{180^o} \\=\dfrac{3\pi}{2}$ Substitute the given values of the radius and $\theta$ to obtain: $A=\frac{1}{2}r^2\theta \\A=\frac{1}{2}(90.0^2)(\frac{3\pi}{2}) \\A=19,085.17537 \\\color{blue}{A\approx 19,085.2 \space km^2}$
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