Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 6 - Trigonometric Functions - 6.1 Angles and Their Measure - 6.1 Assess Your Understanding - Page 363: 98

Answer

$300\pi\approx942.48\ in^2$

Work Step by Step

Given $r_1=30, r_2=30-24=6, \theta=125^\circ=\frac{25\pi}{36}$, the area swept by the blade is the difference of the total swept by $r_1$ and the uncovered area from $r_2$, thus $A=\frac{1}{2}(r_1^2-r_2^2)\theta=\frac{1}{2}(30^2-6^2)(\frac{25\pi}{36})=300\pi\approx942.48\ in^2$
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