Question

The areas of two circle are in ratio 4:9. The ratio of their circumference is?​

Answer 1

Answer: 2:3

Step-by-step explanation:

πr1^2 / πr2^2 = 4/9

r1^2/r2^2 = 4/9

r1/r2 = 2/3

Circumference ratio= 2πr1/2πr2

= r1/r2

= 2/3 = 2:3

Answer 2

Radius of first circle = R1

Radius of second circle = R2

$\frac{area \: of \:first \: circle }{area \: of \: second \: circle} = \frac{4}{9} \\ \frac{\pi \:R {1}^{2} }{\pi \:R2² } = \frac{4}{9} \\ \frac{R1²}{R2²} = \frac{2²}{3²} \\ \frac{R1}{R2} = \frac{2}{3}$

$\frac{circumference \: of \: first \: circle }{circumference \: of \: second \: circle } = \frac{2\pi \: R1}{2\pi \: R2} \\ \\ \frac{circumference \: of \: first \: circle }{circumference \: of \: second \: circle } = \frac{r1}{r2} \\ \\ \frac{circumference \: of \: first \: circle }{circumference \: of \: second \: circle } = \frac{2}{3}$