Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises: 43

Answer

$6\pi$

Work Step by Step

Step 1: The formula to be used here is $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of the sector of the circle of radius $r$ and central angle $\theta$. Step 2: Since $\theta$ is not given, we will transform the equation to one containing $r$ and $s$: $A=\frac{1}{2}×r×r×\theta=\frac{1}{2}×r×(r×\theta)=\frac{1}{2}rs$ Step 3: Substituting the values of $r$ and $s$ into the equation: $A=\frac{1}{2}rs=\frac{1}{2}×6×2\pi=6\pi$ Step 4: Therefore, the area is $6\pi$.
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