question_answer

The circumference of two circles are in the ratio 3:4. Find the ratio of their areas.

Answer:

Let the radii of circles are\[{{r}_{1}}\,and\text{ }{{r}_{2}}\]. According to questions, \[\frac{2\pi {{r}_{1}}}{2\pi {{r}_{2}}}=\frac{3}{4}\] \[=\frac{3}{4}\]                                                                                                                           Ratio of areas \[=\frac{\pi {{r}_{1}}^{2}}{\pi {{r}_{2}}^{2}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\] =\[{{\left( \frac{3}{4} \right)}^{2}}\] \[=\frac{9}{4}=9:4\]