Question

If the area of a sector is one-twelfth that of a complete circle, then the angle of the sector is :

• A. 36°
• B. 30°
• C. 60°
• D. 45°

Answer 1

The Correct Option is B

Step 1: Understand the problem:
We are given that the area of a sector is one-twelfth of the area of a complete circle. We are tasked with finding the angle of the sector.

Step 2: Use the formula for the area of a sector:
The area \( A_{\text{sector}} \) of a sector with radius \( r \) and angle \( \theta \) (in degrees) is given by the formula:
\[ A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2 \] The area of the complete circle is:
\[ A_{\text{circle}} = \pi r^2 \] We are told that the area of the sector is one-twelfth of the area of the complete circle, so we can set up the equation:
\[ A_{\text{sector}} = \frac{1}{12} \times A_{\text{circle}} = \frac{1}{12} \times \pi r^2 \] Substitute the formula for \( A_{\text{sector}} \) into this equation:
\[ \frac{\theta}{360^\circ} \times \pi r^2 = \frac{1}{12} \times \pi r^2 \] We can cancel out \( \pi r^2 \) from both sides:
\[ \frac{\theta}{360^\circ} = \frac{1}{12} \]

Step 3: Solve for \( \theta \):
Now, solve for \( \theta \):
\[ \theta = \frac{360^\circ}{12} = 30^\circ \]

Step 4: Conclusion:
The angle of the sector is \( \boxed{30^\circ} \).