Question

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

Answer 1

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