Question

The area of a sector of angle ${\theta }^{\circ }$ of a circle with radius $R$ is

(a) $\frac{2\pi R\theta }{180}$

(b) $\frac{\pi R^2\theta }{180}$

(c) $\frac{2\pi R\theta }{360}$

(d) $\frac{\pi R^2\theta }{360}$

Answer 1

The correct option is D. $\frac{\pi R^2\theta }{360}$

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

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

Now, we know that,

Angle swept by ${360}^{\circ }$ at the centre $=\pi R^2$

Angle swept by $1^{\circ }$ at the centre $=\frac{\pi R^2}{{360}^{\circ }}$

Therefore, Angle swept by ${\theta }^{\circ }$ at the centre $=\frac{\pi R^2}{{360}^{\circ }}\times {\theta }^{\circ }$