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Q. 67

Expert-verifiedFound in: Page 479

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 ****$\mathbf{70}\mathbf{}{\mathit{m}}^{\mathbf{2}}$. Find the radius of the circle.**

The radius of the circle is **5****.35 meters**.

Central angle $\theta =140\xb0$ and $\text{Area}=70{m}^{2}$.

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.

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

To calculate the radius of the sector

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

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