Question

The ratio of the radii of two circles is $5:6$. What is the ratio of their circumferences?

Answer 1

Let $r_1$ be the radius of one circle.

Let $r_2$ be the radius of another circle.

$c_1$ be the circumference of one circle.

$c_2$ be the circumference of another circle.

$\frac{r_1}{r_2}=$ $\frac{5}{6}$

$\therefore$ $c_1=2\pi r_1$ and $c_2=2\pi r_2$

$\therefore$ $\frac{c_1}{c_2}$ =$\frac{2\pi r_1}{2\pi r_2}$

$\Rightarrow \frac{c_1}{c_2}$ $=\frac{r_1}{r_2}$

$\Rightarrow \frac{c_1}{c_2}$ =$\frac{5}{6}$