Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A circle and a square have the same area. The ratio of the side of the square and the radius of the circle is
(a)$\sqrt{22}: \sqrt{7}$
(b)$\sqrt{\pi}: 1$
(c)$1: \pi$
(d)$\sqrt{7}: \sqrt{22}$
Answer
Answer (as printed): B
Explanation
Let the area of each of the circle and the square be $x$ sq.units. Let the radius of the circle be $r$ units and the side of the square be $a$ unit. Then, $\pi r^{2}=x \Rightarrow r=\sqrt{\frac{x}{\pi}}$. And, $a^{2}=x \Rightarrow a=\sqrt{x}$. $$\text { ∴ } \text { Required ratio }=\frac{\sqrt{x}}{\sqrt{\frac{x}{\pi}}}=\sqrt{\pi}: 1 .$$
Explanation as extracted from the printed page; notation may be imperfect.