Question

Find the area of a sector with central angle$\frac{\mathbf{2}\mathbf{\pi }}{\mathbf{3}}$ rad in acircle of radius 10 m.

Short answer

The area of the circular sector for the given radius and central angle is $\frac{\mathbf{100}\mathbf{\pi }}{\mathbf{3}}{\mathit{m}}^{\mathbf{2}}$.

Step-by-step solution

Step 1. Given information.

The radius of circle $10m$and central angle $\theta$ is $\frac{2\pi }{3}$.

Step 2. Write the concept.

Use the relation between area and central$\theta$ is:

$A=\frac{1}{2}{r}^2\theta$

Step 3. Determining the area.

Putting the values in above formula:

$$\begin{gathered} A=\frac{1}{2}{r}^2\theta \\ A=\frac{1}{2}\times {10}^2\times \frac{2\pi }{3} \\ A=\frac{100\pi }{3}{m}^2 \end{gathered}$$