Question

The ratio of areas of two circles is 9:25.Determine ratio of their circumferences.

Answer 1

2πr : 2πr
2 X 22/7 X 9 : 2 X 22/7 X 25
2 and 22/7 get cancelled.
 = 9:25
= 3:5

Answer 2

Let the radius of first circle be r1, and the radius of second circle be r2.

The ration of the circumference of two circles will be $2 \pi r_1 : 2 \pi r_2$

or, $r_1 : r_2$

By the question, $\dfrac{\pi {r_1}^2}{\pi {r_2}^2} = \dfrac{9}{25}$

or, $\dfrac{{r_1}^2}{{r_2}^2} = \dfrac{9}{25}$
or, $\dfrac{{r_1}}{{r_2}} = \dfrac35$

So, the ration of circumference is 3:5