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Q. 67

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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

The area of a sector of a circle with a central angle of $140^{\circ}$ is $70 m^{2}$ . Find the radius of the circle.

The radius of the circle is 5.35 meters.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Central angle $θ = 140 °$ and $Area = 70 m^{2}$ .

Step 2. Write the concept.

First, convert the central angle into radian by multiplying $\frac{π}{180}$ and then use the formula of the area of the circular sector to calculate the radius of the circle.

Step 3. Determining the area.

$\begin{array}{rcl} The central angle in rad is theta & = & \frac{π}{180} \times 140 \\ = & \frac{7 π}{9} \end{array}$

To calculate the radius of the sector

$A = \frac{1}{2} r^{2} θ r^{2} = \frac{2 A}{θ} r^{2} = \frac{70}{7 π / 9} r = 5.35 m$

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