The circumference of two circle are in the ratio 2 : 3 find the ratio of their areas

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The circumference of two circles are in ratio 2:3. Find the ratio of their areas

Let radius of two circles be 𝑟1 and 𝑟2 then their circumferences will be 2𝜋𝑟1 : 2𝜋𝑟2
= 𝑟1: 𝑟2

But circumference ratio is given as 2 : 3

𝑟1: 𝑟2 = 2: 3

Ratio of areas = 𝜋𝑟22: 𝜋𝑟22

`= (r_1/r_2)^2`

`=(12/3)^2`

`= 4/9`

= 4:9

∴ 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑎𝑟𝑒𝑎𝑠 = 4 ∶ 9

Concept: Circumference of a Circle

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The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

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