Find the radius of the circle whose area is twice the area of the circle of radius 14 cm

Dear Student,        

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{Radius} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{circle}, \mathrm{r} = 14 \mathrm{cm} \\ \mathrm{Area} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{circle}, \mathrm{A} = {\mathrm{\pi r}}^2 = \frac{22}{7}\times 14\times 14 = 22 \times 28 = 616 {\mathrm{cm}}^2 \\ \mathrm{Let} {\mathrm{r}}_1 \mathrm{be} \mathrm{the} \mathrm{radius} \mathrm{of} \mathrm{the} \mathrm{bigger} \mathrm{circle}. \\ \mathrm{Area} \mathrm{of} \mathrm{bigger} \mathrm{circle}, {\mathrm{A}}_1 = {{\mathrm{\pi r}}_1}^2 \\ \mathrm{Now}, {\mathrm{A}}_1 = 2\mathrm{A} \\ \Rightarrow {{\mathrm{\pi r}}_1}^2 = 2\times 616 \\ \Rightarrow \frac{22}{7}\times {{\mathrm{r}}_1}^2 = 1232 \\ \Rightarrow {{\mathrm{r}}_1}^2 = 392 \\ \Rightarrow {\mathrm{r}}_1 = \sqrt{7\times 7\times 2\times 2\times 2} \\ \Rightarrow {\mathrm{r}}_1 = 14\sqrt{2} \mathrm{cm} \end{gathered}$$

Hope this would clear your doubt.                                                               

Do let us know in case of any further concerns.                                                               

Regards