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 \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{\pi {{r}_{1}}^{2}}{\pi {{r}_{2}}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\] \[={{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{81}\]

"> 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 \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{\pi {{r}_{1}}^{2}}{\pi {{r}_{2}}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\] \[={{\left( \frac{4}{9} \right)}^{2}}=\frac{16}{81}\]

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If the ratio of circumference of two circle is \[4:9,\]what is the ratio of their areas?

7th Class Mathematics in 7th Class 10 months ago

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

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