#### Question

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

#### Solution

Let radius of two circles be 𝑟_{1} and 𝑟_{2} then their circumferences will be 2𝜋𝑟_{1} : 2𝜋𝑟_{2}

= 𝑟_{1}: 𝑟_{2}

But circumference ratio is given as 2 : 3

𝑟_{1}: 𝑟_{2} = 2: 3

Ratio of areas = 𝜋𝑟_{2}^{2}: 𝜋𝑟_{2}^{2}

`= (r_1/r_2)^2`

`=(12/3)^2`

`= 4/9`

= 4:9

∴ 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑎𝑟𝑒𝑎𝑠 = 4 ∶ 9

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#### APPEARS IN

Solution The Circumference of Two Circles Are in Ratio 2:3. Find the Ratio of Their Areas Concept: Perimeter and Area of a Circle.