Question

The ratio of the areas of two circles is $4:9$. Draw two such circles after calculating the ratio of their radii. The ratio of their radii is

• A. $1:3$
• B. $1:2$
• C. $2:3$
• D. $1:1$

Answer 1

Answer: (C)

$2:3$

Area of circle is $\pi r^2$

Therefore $\frac{A_1}{A_2}=\frac{4}{9}=\frac{\pi {r_1}^2}{\pi {r_2}^2}$ [Given area ratio]

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

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

ratio of their radii is $2:3$

So, option C is the answer.