Question

A sector of ${120}^{\circ }$ cut out from a circle has an area of $9\frac{3}{7}$ sq cm The radius of the circle is

• A. 3 cm
• B. 2.5 cm
• C. 3.5 cm
• D. 3.6 cm

Answer 1

The correct option is A 3 cm

we have
$\frac{x}{360}\times \pi r^2=9\frac{3}{7}$
$\frac{120}{360}\times \frac{22}{7}\times r^2=\frac{66}{7}$
$r^2=\frac{66}{7}\times \frac{360}{120}\times \frac{7}{22}$
= 9
$r=\sqrt{9}=3cm$