Question

If the ratio of the areas of two circles is $1:4$, then the ratio of their circumferences is ...................

• A. $1:4$
• B. $2:3$
• C. $1:2$
• D. $3:2$

Answer 1

Answer: (C)

$1:2$

For 1st circle, radius $=r_1$, circumference $=C_1,$ Area $=A_1$
For 2nd circle, radius $=r_2$, circumference $=C_2$, Area $=A_2$
Given, $\frac{A_1}{A_2}=\frac{1}{4}⟹\frac{\pi (r_1{)}^2}{\pi (r_2{)}^2}=\frac{1}{4}⟹\frac{r_1}{r_2}=\frac{1}{2}.....\left(1\right)$
Now,
$\frac{C_1}{C_2}=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}=\frac{1}{2}$ ........ [by $\left(1\right)$]

Hence, ratio of circumference of circles is $1:2$