Question

The area of a sector with radius 14 cm is 154 $c{m}^2$. The central angle of the sector (in degrees) is

• A. 90${}^{\circ }$
• B. 180${}^{\circ }$
• C. 45${}^{\circ }$
• D. 270${}^{\circ }$

Answer 1

The correct option is A

90${}^{\circ }$

$\text{Area of a sector of radius}r\text{and central angle}\theta \text{degrees}=\frac{\theta }{360}\times \pi r^2$

$⟹\frac{\theta }{360}\times \pi r^2=154$

i.e., $\frac{\theta }{360}\times \frac{22}{7}\times 14\times 14=154$

$⟹\theta =\frac{154\times 360}{22\times 2\times 14}={90}^{\circ }$