The ratio of the radii of two circles is 3 : 2. What is the ratio of their circumferences? (S.S.C., 2010)

### Concept & Formula The circumference of a circle is directly proportional to its radius. Therefore, the ratio of the circumferences of two circles is exactly the same as the ratio of their radii. $$ \frac{C_1}{C_2} = \frac{2\pi r_1}{2\pi r_2} = \frac{r_1}{r_2} $$ ### Step-by-Step Solution 1. **Given:** The ratio of the radii of two circles is $3 : 2$. Let them be $r_1$ and $r_2$. 2. **Calculate the ratio of circumferences:** Ratio of circumferences = $\frac{2\pi r_1}{2\pi r_2} = \frac{r_1}{r_2} = \frac{3}{2}$. The ratio is $3 : 2$. ### Exam Strategy & Shortcut For circles, the ratio of radii is ALWAYS equal to the ratio of diameters and the ratio of circumferences. No calculation is needed. ### Common Pitfall Squaring the ratio ($9 : 4$) is a common error made by students who confuse the relationship of circumferences with the relationship of areas. ### Final Answer Therefore, the correct answer is **3 : 2**.