A) \[9:4\]
B) \[16:81\]
C) \[4:9\]
D) \[2:3\]
Correct Answer: B
Solution :
\[\left. \begin{align} & Circle-1:{{C}_{1}}=2\pi {{r}_{1}} \\ & Circle-2:{{C}_{2}}=2\pi {{r}_{2}} \\ \end{align} \right\}\]Now, \[a\frac{2\pi {{r}_{1}}}{2\pi {{r}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{4}{9};\]Area ratio \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{\pi {{r}_{1}}^{2}}{\pi {{r}_{2}}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\] \[={{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{81}\]
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