Question

The areas of two circles are in the ratio $121:49$. Find the ratio of their circumferences.

• A. $\pi$
• B. $\frac{12\pi }{3}$
• C. $\frac{11}{7}$
• D. None

Answer 1

Answer: (C)

$\frac{11}{7}$

Let $r_1,c_1$ and $A_1$ be the radius, circumference and area of 1st circle, respectively and $r_2,c_2$ and $A_2$ be the radius, circumference and area of the 2nd circle, respectively.

$\therefore \frac{A_1}{A_2}=\frac{\pi {r_1}^2}{\pi {r_2}^2}$

$\therefore \frac{121}{49}=\frac{{r_1}^2}{{r_2}^2}$

$\therefore \frac{r_1}{r_2}=\frac{11}{7}$ ....(1)

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

$\therefore \frac{c_1}{c_2}=\frac{r_1}{r_2}=\frac{11}{7}$ ....from (1)