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Q. 67

Expert-verified
Found in: Page 479

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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

The radius of the circle is 5.35 meters.

See the step by step solution

## Step 1. Given information.

Central angle $\theta =140°$ and $\text{Area}=70{m}^{2}$.

## Step 2. Write the concept.

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

## Step 3. Determining the area.

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

To calculate the radius of the sector

$A=\frac{1}{2}{r}^{2}\theta \phantom{\rule{0ex}{0ex}}{r}^{2}=\frac{2A}{\theta }\phantom{\rule{0ex}{0ex}}{r}^{2}=\frac{70}{7\pi /9}\phantom{\rule{0ex}{0ex}}r=5.35m$