Question

A sector of a circle having a radius 14 cm has area 154 cm². Find the angle of the sector.

• A. 90°
• B. 120°
• C. 150°
• D. 180°

Answer 1

Answer:

A. 90°

For a sector of a circle:

The area of a sector is given by:

$\text{Area of sector}=\frac{\theta}{360^\circ},\pi r^2$

Given:

• Area $(=154\ \text{cm}^2)$

• Radius $(r=14\ \text{cm})$

Substituting:

$154=\frac{\theta}{360}\times \frac{22}{7}\times 14^2$

$154=\frac{\theta}{360}\times 616$

$\frac{\theta}{360}=\frac{154}{616}=\frac{1}{4}$

$\theta=\frac{360}{4}=90^\circ$