Question

The area of a sector of a circle with a central angle of$\frac{\mathbf{5}\mathbf{\pi }}{\mathbf{12}}$ rad is $\mathbf{20}{\mathit{m}}^{\mathbf{2}}$. Find the radius of the circle.

Short answer

If the area of a sector of a circle with a central angle$\frac{5\pi }{12}$ of$20m^2$ is then the radius of the circle for the given values is 5.28 m.

Step-by-step solution

Step 1. Given information.

Central angle $\theta =\frac{5\pi }{12}$ and area $\text{A}=20m^2$ .

Step 2. Write the concept.

The central angle in rad is$\theta =\frac{5\pi }{12}$

Use the given formula to calculate the radius

$$\begin{gathered} \text{A}=\frac{1}{2}{r}^2\theta \\ {r}^2=\frac{2A}{\theta } \end{gathered}$$

Step 3. Determining the values of radius.

Putting the values in the above formula:

$$\begin{gathered} \text{A}=\frac{1}{2}{r}^2\theta \\ {r}^2=\frac{2A}{\theta } \\ r=\sqrt{\frac{2\times 20\times 12}{5\pi }} \\ r=\sqrt{\frac{96}{\pi }} \\ r=5.528m \end{gathered}$$