Question

Tick the correct answer in the following.
Area of a sector of angle $p^{\circ }$ of a circle with radius $R$ is:
1. $\frac{p^{\circ }}{{180}^{\circ }}\times 2\pi R$
2. $\frac{p^{\circ }}{{360}^{\circ }}\times \pi R^2$
3. $\frac{p^{\circ }}{{360}^{\circ }}\times 2\pi R$
4. $\frac{p^{\circ }}{{720}^{\circ }}\times 2\pi R^2$

Answer 1

The correct option is 2. $\frac{p^{\circ }}{{360}^{\circ }}\times \pi R^2$

Let $O$ be the centre of the circle with radius $R$ units.

Let $p^{\circ }$ be the angle of the sector of the circle.

Now, we know that,

Area of a circle at an angle swept by ${360}^{\circ }$ at the centre = $\pi R^2$

Now area of a sector at angle swept by $1^{\circ }$ at the centre = $\frac{\pi R^2}{{360}^{\circ }}$

Therefore, Area of a sector at an angle swept by $p^{\circ }$ at the centre = $\frac{\pi R^2}{{360}^{\circ }}\times p^{\circ }$