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 362: 82


$6.928\text{ cm}.$

Work Step by Step

Here, $r$ denotes the radius of the sector of the circle. The Area of sector can be computed by the formula: $A=\frac{\theta}{2}\cdot r^2$ where $\theta$ is the central angle measure in radians. Hence here we have $6=\frac{\frac{1}{4}}{2}\cdot r^2\\6=\frac{1}{8}\cdot r^2\\6(8)=(8)\frac{1}{8}\cdot r^2\\48=r^2.$ Take the square root of both sides: $\sqrt{r^2}=\pm\sqrt{48}\\r=\pm\sqrt{48}\\r=\pm6.9282\approx6.928\text{ cm}$ Since $r$ is a radius, it can't be negative. Thus, $r\approx6.928\text{ cm}.$
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