Question

Find the area of the sector of a circle of radius $5cm$, if the corresponding arc length is $3.5cm$

Answer 1

Solve for area of the given sector

Given,

1. Radius of the circle $r=5cm$
2. Arc length of the sector $l=3.5cm$

Step 1: Find center angle

Let the central angle (in radians) be $\theta$

$\therefore$Arc length $=r\times \theta$

$\Rightarrow \theta =\frac{l}{r}$$=\frac{3.5}{5}=0.7radian$

Step 2: Find area of the sector

We know that, area of the sector $=\frac{1}{2}\times r^2\theta$

$$\begin{gathered} =\frac{1}{2}\times {\left(5\right)}^2\times 0.7 \\ =8.75c{m}^2 \end{gathered}$$

Hence, the area of the given sector of circle is $8.75c{m}^2$