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Q. 69

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Precalculus Mathematics for Calculus

Found in: Page 479

Book edition 7th Edition

Author(s) James Stewart, Lothar Redlin, Saleem Watson

Pages 948 pages

ISBN 9781337067508

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Short Answer

A sector of a circle of radius 80 miles has an area of $1600 {miles}^{2}$ . Find the central angle (in radians) of the sector.

The central angle for the given radius and the circular area is $\frac{1}{2}$ radian.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Area $A = 1600 {miles}^{2}$ and the radius $r = 80$ miles.

Step 2. Write down the concept.

Use the formula of the circular area $A = \frac{1}{2} r^{2} θ$ .

Step 3. Determining the angle

Central angle $θ = \frac{2 A}{r^{2}}$

$θ = 2 \times \frac{1600}{80^{2}}$

$θ = \frac{1}{2}$ radian.

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