Question

If the ratio of areas of two circles is $25:36$, the ratio of their circumference is

• A. $36:25$
• B. $5:6$
• C. $6:5$
• D. $4:5$

Answer 1

The correct option is B $5:6$

Let the radii of two given circles be $r$ and $R$ respectively.
$\therefore$ Ratio of their areas $=25:36$
$\frac{\pi \times r^2}{\pi R^2}=\frac{25}{36}$
$\sqrt{\frac{r^2}{R^2}}=\sqrt{\frac{25}{36}}$
$\frac{r}{R}=\frac{5}{6}$
Ratio of their circumferences:
$=\frac{2\pi r}{2\pi R}=\frac{r}{R}=\frac{5}{6}$
$5:6$