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: Problem Definition:
A sector's area is given as 1/12th of a full circle's area. The objective is to determine the sector's angle.

Step 2: Sector Area Formula Application:
The area \( A_{\text{sector}} \) of a sector with radius \( r \) and angle \( \theta \) (in degrees) is calculated as:
\[A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2\]The area of the complete circle is:
\[A_{\text{circle}} = \pi r^2\]Given that \( A_{\text{sector}} = \frac{1}{12} \times A_{\text{circle}} \), we can write:
\[A_{\text{sector}} = \frac{1}{12} \times \pi r^2\]Substituting the sector area formula:
\[\frac{\theta}{360^\circ} \times \pi r^2 = \frac{1}{12} \times \pi r^2\]Canceling \( \pi r^2 \) from both sides yields:
\[\frac{\theta}{360^\circ} = \frac{1}{12}\]

Step 3: Angle Calculation:
Solving for \( \theta \):
\[\theta = \frac{360^\circ}{12} = 30^\circ\]

Step 4: Final Result:
The sector's angle is \( \boxed{30^\circ} \).