Question

The area of a circle is $\mathbf{600}{\mathit{m}}^{\mathbf{2}}$. Find the area of a sector of this circle that subtends a central angle of 3 rad.

Short answer

The value of the circular area for the given area and central angle is almost $\mathbf{285}\mathbf{.}\mathbf{7}{\mathit{m}}^{\mathbf{2}}$.

Step-by-step solution

Step 1. Given information.

Area of circle $a=600m^2$ and central angle$\text{theta}=3$ rad

Step 2. Write the concept.

The area of the circle$a=\pi r^2$

So, the radius of the circle is

$r=\sqrt{\frac{a}{\pi }}$

Now, the circular area is given by

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

Step 3. Determining the area of sector.

Putting the value of the area in above formula

$$\begin{gathered} r=\sqrt{\frac{600}{\pi }} \\ r=13.8m \end{gathered}$$

Putting the values of $r$in

$$\begin{gathered} A=\frac{1}{2}{r}^2\theta \\ A=\frac{1}{2}\times {13.8}^2\times 3 \\ A=285.7m^2 \end{gathered}$$