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: $2\pi :1$
Option 2: $1:\sqrt{\pi}$
Option 3: $\sqrt{\pi}:1$
Option 4: $1:\pi$
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Correct Answer: $\sqrt{\pi}:1$
Solution :
Let the radius of the circle = $r$
Side of square = $a$
Given: Area of the circle = Area of square
⇒ $\pi r^2=a^2$
⇒ $\frac{a^2}{r^2}=\pi$
⇒ $\frac{a}{r}=\frac{\sqrt{\pi}}{1}$
⇒ $a:r=\sqrt \pi:1$
Hence, the correct answer is $\sqrt{\pi}:1$.
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