Question

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

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

Answer 1

Answer: (A)

$3cm$

Area of sector $=9\frac{3}{7}{cm}^2=\frac{66}{7}{cm}^2$

$\Rightarrow \frac{\theta }{{360}^0}\times \pi r^2=\frac{66}{7}\Rightarrow \frac{{120}^0}{{360}^0}\times \frac{22}{7}\times r^2=\frac{66}{7}\Rightarrow r^2=\frac{66\times 3}{22}=9$

$r=\sqrt{9}=3cm$

$\therefore$ Radius $=3$ cm