Question

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

• A. $269.5c{m}^2$
• B. $1078c{m}^2$
• C. $539c{m}^2$
• D. $1617c{m}^2$

Answer 1

Answer: (A)

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