Question

If a sector of a circle of diameter $21cm$ subtends an angle of ${120}^{\circ }$ at the centre, then what is its area ?

• A. $115.5c{m}^2$.
• B. $84c{m}^2$.
• C. $85.5c{m}^2$.
• D. $78c{m}^2$.

Answer 1

The correct option is A $115.5c{m}^2$.

Area of sector $=\frac{\theta }{360}\times \pi \times r^2$

$=\frac{120}{360}\times \pi \times (\frac{21}{2}{)}^2$

Thus area $=\frac{1}{3}\times \frac{22}{7}\times \frac{441}{4}=115.5c{m}^2$