Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A circle is inscribed in a square of side 54 cms and another circle circumscribes the same square. Then the ratio of circumferences of the bigger circle to the smaller circle is
(a)$1: \sqrt{2}$
(b)$\sqrt{2}: 1$
(c)$\sqrt{3}: 1$
(d)None of these
Answer
Answer (as printed): B
Explanation
Let $r_{1}$ and $r_{2}$ be the radii of the inscribed and circumscribed circles respectively. Then, $r_{1}=\frac{5}{2} \mathrm{cm}$. $$\begin{aligned} & r_{2}=\frac{1}{2} \times \text { diagonal of the square }=\frac{1}{2} \times 5 \sqrt{2}=\frac{5 \sqrt{2}}{2} \mathrm{cm} . \\ & \therefore \quad \text { Required ratio }=\frac{2 \pi \times \frac{5 \sqrt{2}}{2}}{2 \pi \times\left(\frac{5}{2}\right)}=\sqrt{2}: 1 . \end{aligned}$$