Question : In the given figure, the length of arc AB is equal to twice the length of radius $r$ of the circle. Find the area of sector OAB in terms of the radius $r$.
Option 1: $3r$
Option 2: $2r$
Option 3: $ \pi r^2$
Option 4: $ r^2$
Correct Answer: $ r^2$
Solution :
Let the radius of the circle be $r$
Here, we know that the length of the arc = $2r$
$⇒ l = r × \theta$
Where $\theta$ is in radian and $l$ is the length of the arc.
$⇒ 2r = r × \theta$
$⇒ \theta = 2$
Area of the sector = $\frac{\theta}{360} \times \pi r^2$
Area of the sector = $\frac{2}{360} × 180 × r^2$ [As $\pi = 180°$]
Area of the sector = $r^2$
Hence, the area of the sector OAB in terms of the radius is $r^2$.
Hence, the correct answer is $r^2$.
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