Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 6 - Section 6.1 - Angle Measure - 6.1 Exercises: 70

Answer

Area of the sector = 286.48 $m^{2}$

Work Step by Step

Given- Area of the circle =600 $m^{2}$ Let radius be 'r' m Therefore Area of the circle = $\pi r^{2}$ = 600 or $r^{2}$ = $\frac{600}{\pi}$ Now we need to calculate the area 'A' of a circular sector of this circle that subtends a central angle of 3 rad. We know that- Area of sector, A = $\frac{1}{2} r^{2} \theta$ or A = $\frac{1}{2}\times r^{2}\times \theta$ or A = $\frac{1}{2}\times \frac{600}{\pi}\times 3$ (substituting for $r^{2}$ and $\theta$) A = $\frac{900}{\pi}$ = 286.48 $m^{2}$ Therefore, area of the sector, A = 286.48 $m^{2}$
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