Question

If the ratio of areas of two circles is $16:25$, the ratio of their circumference is

• A. $25:16$
• B. $5:4$
• C. $4:5$
• D. $3:5$

Answer 1

The correct option is C $4:5$

Let the radii of the circles be $r_1$ & $r_2$ respectively.

Then, their circumferences are $2\pi r_1$ & $2\pi r_2$, respectively.

So, their ratio=$2\pi r_1:2\pi r_2=r_1:r_2$.

Again, the areas of the circles are $\pi {\left(r_1\right)}^2$ & $\pi {\left(r_2\right)}^2$.

Then, their ratio $=\pi {\left(r_1\right)}^2:\pi {\left(r_2\right)}^2={\left(r_1\right)}^2:{\left(r_2\right)}^2=16:25$ ...(given).

$\therefore \left(r_1\right):\left(r_2\right)=\sqrt{16:25}=\pm (4:5)$

We reject the negative value of r's since the radius is a length.

$\therefore \left(r_1\right):\left(r_2\right)=(4:5)$.