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: 63

Answer

63 (a). 44.68 square unit 63 (b). 25 square unit

Work Step by Step

Given- Central angle of the sector. $\theta$ = $80^{\circ}$ or, $\theta$ = $80\times\frac{\pi}{180}$ = $\frac{4\pi}{9}$ rad radius, r = 8 unit A = ? We know that area 'A' of a circular sector with central angle $\theta$ rad and radius 'r' is given by- A = $\frac{1}{2} r^{2} \theta$ = $\frac{1}{2}\times 8^{2}\times \frac{4\pi}{9}$ =$\frac{64\times2\pi}{9}$ = $\frac{128\pi}{9}$ square unit = 44.68 square unit 63 (b). Given- Central angle of the sector. $\theta$ = 0.5 rad radius, r = 10 unit A = ? We know that area 'A' of a circular sector with central angle $\theta$ rad and radius 'r' is given by- A = $\frac{1}{2} r^{2} \theta$ = $\frac{1}{2}\times 10^{2}\times 0.5$ =$\frac{100\times0.5}{2}$ = $\frac{50}{2}$ square unit = 25 square unit
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