Question

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.

Short answer

The radius of the circle is 5.35 meters.

Step-by-step solution

Step 1. Given information.

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

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.

$\begin{array}{rcl}\text{Thecentralangleinradistheta}& =& \frac{\pi }{180}\times 140\\ & =& \frac{7\pi }{9}\end{array}$

To calculate the radius of the sector

$$\begin{gathered} A=\frac{1}{2}{r}^2\theta \\ {r}^2=\frac{2A}{\theta } \\ {r}^2=\frac{70}{7\pi /9} \\ r=5.35m \end{gathered}$$