Question

The ratio of the circumference of two circles is $2:3$. What is the ratio of their areas?

• A. $4:9$
• B. $2:3$
• C. $9:4$
• D. $3:2$

Answer 1

Answer: (A)

$4:9$

Let the radii of two circles be $r_1$ and $r_2$.

Then, according to question, we have

$\frac{2\pi r_1}{2\pi r_2}=\frac{2}{3}$

$\Rightarrow \frac{r_1}{r_2}=\frac{2}{3}$

Squaring both the sides, we get,

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

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

So, the ratio of the areas of two circles is $4:9$