Question

the area of a circle is 100 time the area of another circle. find the ratio of their circumference.

Answer 1

$A_1=100A_2$

$\Rightarrow \frac{A_1}{A_2}=100$

$\Rightarrow \frac{\pi r_1^2}{\pi r_2^2}=100$

$\Rightarrow \frac{r_1}{r_2}=10$

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

$=\frac{r_1}{r_2}=\frac{10}{1}$.