The areas of two circles are in the ratio 4:9. What is the ratio between their circumferences?

Given:

Ratio of areas of two circles = 2:3

Let the two circles be C₁ and C₂ with radii ‘r₁’ and ‘r₂’.

∵ Area of circle = πr²

∴ Area of C₁ = πr₁²

and Area of C₂ = πr₂²

⇒ =

⇒ =

Taking square root on both sides, we get

⇒ =

⇒ =

Multiplying and dividing L.H.S. by ‘π’, we get

⇒ =

Multiplying and dividing L.H.S. by ‘2’, we get

⇒ =

As Circumference of circle = 2πr

⇒ =

Hence, the ratio between the circumferences of C₁ and C₂ is 2:3.