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: $\sqrt\pi:1$
Option 2: $1:\sqrt\pi$
Option 3: $(\pi)^2:1$
Option 4: $1:\sqrt2\pi$
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Correct Answer: $\sqrt\pi:1$
Solution :
Given: A circle and a square have the same area.
We know that the area of the square is $a^2$, where $a$ is its side, and the area of the circle is $\pi\times r^2$, where $r$ is its radius.
According to the question,
$\pi\times r^2=a^2$
⇒ $\pi=\frac{a^2}{r^2}$
⇒ $\sqrt\pi=\frac{a}{r}$
The ratio of the square's side to the circle's radius is $\sqrt\pi:1$.
Hence, the correct answer is $\sqrt\pi:1$.
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