Question

The length of an arc subtending an angle of measure ${60}^0$ at the centre of a circle whose area is $616c{m}^2$ is........

• A. $\frac{22}{3}$
• B. $66$
• C. $\frac{44}{3}$
• D. $33$

Answer 1

Answer: (C)

$\frac{44}{3}$

$\theta ={60}^o$

Area of circle $=616c{m}^2$

We know that

$\pi r^2=616$

$r^2=\frac{616\times 7}{22}$

$r^2=196$

$r=14cm$

Length of arc$=\frac{\theta }{{360}^o}\times 2\pi r$

$=\frac{{60}^o}{{360}^o}\times 2\pi \times 14$

$=\frac{1}{6}\times 2\times \frac{22}{7}\times 14$

$=\frac{44}{3}$cm.