Question

The angle subtended by an arc at the centre of a circle is $70^{\circ}$. If the circumference of the circle is $132 cm$, then find the area of the sector formed.

• A. $269.5 cm ^2$
• B. $1078 cm ^2$
• C. $539 cm ^2$
• D. $1617 cm ^2$

Answer 1

Answer: (A)

Let the radius of the circle be $r$.
Given $2 \pi r=132 \Rightarrow r=21 cm$
$\text { Area of the sector } =\frac{70^{\circ}}{360^{\circ}} \times \frac{22}{7} \times 21^2 $
$ =269.5 cm ^2$