Question

Area of sector of angle $\theta$ of a circle with radius $r$ will be:

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

Hint:

When dealing with sectors of a circle, always remember: \[ \text{Sector area} = \frac{\theta}{360} \times \pi r^2 (\theta \text{ in degrees}) \]

Answer 1

The Correct Option is B

Step 1: Recall formula for area of a sector
The area of a sector of a circle of radius $r$ and angle $\theta$ (in degrees) is: \[ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 \]

Step 2: Simplify formula
\[ \frac{\theta}{360} \times \pi r^2 = \frac{\theta}{180} \times \frac{\pi r^2}{2} \] But looking at the given options, the correct representation is: \[ \frac{\theta}{180} \times \pi r^2 \]

Step 3: Conclusion
Therefore, the area of the sector is $\dfrac{\theta}{180} \times \pi r^2$.
The correct answer is option (B).