Question

The radii of two circles are in the ratio 2:3. What is the ratio of their circumferences?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{radii}\mathrm{of}\mathrm{two}\mathrm{circles}\mathrm{be} \\ \mathrm{r}=2\mathrm{x}\mathrm{and}\mathrm{R}=3\mathrm{x} \\ \mathrm{Now},\mathrm{ratio}\mathrm{of}\mathrm{their}\mathrm{circumferences}=\frac{2\mathrm{\pi r}}{2\mathrm{\pi R}}=\frac{\mathrm{r}}{\mathrm{R}}=\frac{2\mathrm{x}}{3\mathrm{x}}=\frac{2}{3} \\ \mathrm{So},\mathrm{the}\mathrm{required}\mathrm{ratio}\mathrm{is}2:3 \end{gathered}$$
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