Question : The areas of a circle and a square are the same. The ratio of the side of the square to the radius of the circle is:
Option 1: $2 π : 1$
Option 2: $1 : \sqrt{π}$
Option 3: $\sqrt{π} : 1$
Option 4: $1 : π$

Question

Question : A circle and a square have the same area. The ratio of the side of the square to the radius of the circle will be:
Option 1: $\sqrt{π} : 1$
Option 2: $1 : \sqrt{π}$
Option 3: $(π)^{2} : 1$
Option 4: $1 : \sqrt{2} π$

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Answer 1

Correct Answer: $\sqrt{π} : 1$

Solution : Let the radius of the circle = $r$
Side of square = $a$
Given: Area of the circle = Area of square
⇒ $π r^{2} = a^{2}$
⇒ $\frac{a^{2}}{r^{2}} = π$
⇒ $\frac{a}{r} = \frac{\sqrt{π}}{1}$
⇒ $a : r = \sqrt{π} : 1$
Hence, the correct answer is $\sqrt{π} : 1$ .

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Question : The areas of a circle and a square are the same. The ratio of the side of the square to the radius of the circle is:Option 1: 2π:1Option 2: 1:πOption 3: π:1Option 4: 1:π

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Question : The areas of a circle and a square are the same. The ratio of the side of the square to the radius of the circle is:
Option 1: $2 π : 1$
Option 2: $1 : \sqrt{π}$
Option 3: $\sqrt{π} : 1$
Option 4: $1 : π$