The circumferences of two circles are in the ratio 2:3. What is the ratio between their areas?

Question

Philoid · Accepted Answer

Given:

Ratio of circumferences of two circles = 2:3

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

∵ Circumference of circle = 2πr

∴ Circumference of C₁ = 2πr₁

and Circumference of C₂ = 2πr₂

⇒ =

Squaring both sides, we get

⇒ =

Multiplying both sides by ‘’, we get

⇒ =

∵ Area of circle = πr²

⇒ =

Hence, the ratio between the areas of C₁ and C₂ is 4:9.