Question

Area of a sector of angle $p$ (in degrees) of a circle with radius $R$ is

• A. $\frac{p}{180°}\times 2\mathrm{\pi R}$
• B. $\frac{p}{180°}\times {\mathrm{\pi R}}^2$
• C. $\frac{p}{360°}\times 2\mathrm{\pi R}$
• D. $\frac{p}{720°}\times 2{\mathrm{\pi R}}^2$

Answer 1

The correct option is D

$\frac{p}{720°}\times 2{\mathrm{\pi R}}^2$

Finding the area of sector:

The area of a sector $=\frac{\theta }{360°}\times {\mathrm{\pi r}}^2$

Given, $\theta =p$ and radius$=R$

Therefore, area of sector $=\frac{p}{360°}\times \pi R^2$

On multiplying and dividing by $2$ simultaneously, we get,

$$\begin{gathered} \frac{p}{360°}\times {\mathrm{\pi R}}^2 \\ =\frac{2p}{360°\times 2}\times {\mathrm{\pi R}}^2 \\ =\frac{p}{720°}\times 2{\mathrm{\pi R}}^2 \end{gathered}$$

Hence, option (D) is correct answer.