Question

The ratio between the circumference of two circles is $4:9$, find the ratio between their areas.

Answer 1

We have,

$\frac{Circumferenceofcircle\left(1\right)}{Circumferenceofcircle\left(2\right)}=\frac{4}{9}$

$\frac{2\pi r_1}{2\pi r_2}=\frac{4}{9}$

$\frac{r_1}{r_2}=\frac{4}{9}$

So,

$\frac{Areaofcircle\left(1\right)}{Areaofcircle\left(2\right)}=\frac{\pi {r_1}^2}{\pi {r_2}^2}$

$=\frac{{r_1}^2}{{r_2}^2}={\left(\frac{4}{9}\right)}^2$

$=\frac{16}{81}$

Hence, this is the answer.