• # question_answer If the ratio of circumference of two circle is $4:9,$ what is the ratio of their areas? A) $9:4$                          B)  $16:81$C) $4:9$              D)  $2:3$

\left. \begin{align} & Circle-1:\,\,{{C}_{1}}=2\pi {{r}_{1}} \\ & Circle-2:\,\,{{C}_{2}}=2\pi {{r}_{2}} \\ \end{align} \right\}Now, $\frac{2\pi {{r}_{1}}}{2\pi {{r}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{4}{9};$ Area ratio $\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{\pi {{r}_{1}}^{2}}{\pi {{r}_{2}}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}$ $={{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{81}$