Question

If the area of a sector of a circle of radius 14 cm is 154 cm\(^2\), then the angle of the sector will be:

• A. 120°
• B. 90°
• C. 60°
• D. 30°

Hint:

Use \( \text{Area} = \frac{\theta}{360} \pi r^2 \). Cross-check using simple ratios — a 90° sector is one-fourth of a circle.

Answer 1

The Correct Option is C

Step 1: Recall the formula.
\[ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 \]
Step 2: Substitute known values.
\[ 154 = \frac{\theta}{360} \times \frac{22}{7} \times 14^2 \] \[ 154 = \frac{\theta}{360} \times \frac{22}{7} \times 196 \] \[ 154 = \frac{\theta}{360} \times 616 \]
Step 3: Simplify.
\[ \theta = \frac{154 \times 360}{616} = \frac{55440}{616} = 90 \] Wait — recalculate carefully: \[ \frac{616}{4} = 154 \Rightarrow \theta = 360/4 = 90° \] Hence, the angle is \( \boxed{90°} \).

Step 4: Conclusion.
The required angle of the sector is \( 90° \).