If the perimeters of a circle and a square are same, then the ratio of their areas is :
2 : π
4 : π
16 : π
π : 4
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Question

If the perimeters of a circle and a square are same, then the ratio of their areas is : 1. 2 : π 2. 4 : π 3. 16 : π 4. π : 4

KnowledgeBoat · Accepted Answer

Given,

Circumference of circle = 2πr

Perimeter of square = 4a

Given,

Perimeter of square = Circumference of circle

⇒ 4a = 2πr

⇒ 2a = πr

⇒ a = $\dfrac{πr}{2}$

Area of circle = πr²

Area of square = a²

= $\Big(\dfrac{πr}{2}\Big)^2$

= $\dfrac{π^2r^2}{4}$

⇒ Area of circle : Area of square

= πr² : $\dfrac{π^2r^2}{4}$

= $\dfrac{πr^2}{\dfrac{π^2r^2}{4}}$

= $\dfrac{4πr^2}{π^2r^2}$

= $\dfrac{4}{π}$

= 4 : π.

Hence, option 2 is the correct option.

Mathematics