Question

Area of the sector of an angle $\theta^\circ$ of a circle with radius $r$ will be

• A. $\dfrac{\theta}{180} \times 2\pi r$
• B. $\dfrac{\theta}{720} \times 2\pi r^2$
• C. $\dfrac{\theta}{180} \times \pi r^2$
• D. $\dfrac{\theta}{360} \times 2\pi r$

Hint:

The area of a sector depends on the fraction of the circle’s angle: $\text{Sector Area} = \dfrac{\theta}{360} \times \pi r^2$.

Answer 1

The Correct Option is C

Step 1: Formula for area of a sector.
The area of a sector is given by: \[ \text{Area} = \frac{\theta}{360} \times \text{Area of circle} \] \[ = \frac{\theta}{360} \times \pi r^2 \] Simplifying, \[ = \frac{\theta}{180} \times \frac{\pi r^2}{2} = \frac{\theta}{360} \times 2\pi r^2 \] But standard form is $\dfrac{\theta}{360} \times \pi r^2$. Step 2: Conclusion.
Hence, the area of the sector = $\dfrac{\theta}{360} \times \pi r^2$.