Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10: 9781285195698
ISBN 13: 978-1-28519-569-8

Chapter 8 - Section 8.5 - More Area Relationships in the Circle - Exercises - Page 379: 25


4.5 cm

Work Step by Step

Given that the exact area of the sector determined by 40$^{\circ}$ arc is $\frac{9}{4}\pi cm^{2}$ We need to find the length of the radius of the circle In circle of radius length r, the area A of a sector whose arc has degree m is A = $\frac{m}{360} \pi r^{2}$ $\frac{9}{4}\pi$ = $\frac{40}{360} \pi r^{2}$ $r^{2}$ = $\frac{81}{4}$ r = $\sqrt \frac{81}{4}$ r = $\frac{9}{2}$ = 4.5 cm The radius of the circle = 4.5 cm
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