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

Given:

Ratio of circumferences of two circles = 2:3

Let the two circles be C_{1} and C_{2} with radii ‘r_{1}’ and ‘r_{2}’.

∵ Circumference of circle = 2πr

∴ Circumference of C_{1} = 2πr_{1}

and Circumference of C_{2} = 2πr_{2}

⇒ =

⇒ =

Squaring both sides, we get

⇒ =

Multiplying both sides by ‘’, we get

⇒ =

∵ Area of circle = πr^{2}

⇒ =

__Hence, the ratio between the areas of C _{1} and C_{2} is 4:9.__

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