39. The area of the circle is 616. An arc subtends an angle of measure 60^o​ at the centre of the circle. Then the length of the arc is _____.
$$\begin{gathered} \left(A\right) \frac{22}{3} \\ \left(B\right) 66 \\ \left(C\right) \frac{44}{3} \\ \left(D\right) 33 \end{gathered}$$

Dear Student,

$$\begin{gathered} Let the radius of the circle be r. \\ Then, Area = {\mathrm{\pi r}}^2 \\ \Rightarrow 616 = \frac{22}{7}{\mathrm{r}}^2 \\ \Rightarrow {\mathrm{r}}^2 = 616 \times \frac{7}{22} = 196 \\ \Rightarrow \mathrm{r} = 14 \\ \therefore \mathrm{Length} \mathrm{of} \mathrm{an} \mathrm{arc} = \frac{\mathrm{\theta }}{360°} \times 2\mathrm{\pi r}, \mathrm{where} \mathrm{\theta } \mathrm{is} \mathrm{the} \mathrm{angle} \mathrm{subtended} \mathrm{by} \mathrm{the} \mathrm{arc} \mathrm{at} \mathrm{the} \mathrm{centre} \mathrm{of} \mathrm{the} \mathrm{circle} \\ = \frac{60}{360} \times 2 \times \frac{22}{7} \times 14 \\ = \frac{1}{6} \times 2 \times 22 \times 2 \\ = \boxed{\frac{\mathbf{44}}{\mathbf{3}}} \end{gathered}$$

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