Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A wire when bent in the form of a square encloses an area of 484 sq. cm. What will be the enclosed area when the same wire is bent into the form of a circle?
(a)462 sq. cm
(b)539 sq. cm
(c)616 sq. cm
(d)693 sq. cm
Answer
Answer (as printed): C
Explanation
Side of the square $=\sqrt{484} \mathrm{cm}=22 \mathrm{cm}$. Perimeter of the square $=(22 \times 4) \mathrm{cm}=88 \mathrm{cm}$. $$\begin{aligned} & 2 \pi R=88 \Leftrightarrow 2 \times \frac{22}{7} \times R=88 \Leftrightarrow R=\left(88 \times \frac{7}{44}\right)=14 \mathrm{cm} . \\ & \therefore \text { Required area }=\pi R^{2}=\left(\frac{22}{7} \times 14 \times 14\right) \mathrm{cm}^{2}=616 \mathrm{cm}^{2} . \end{aligned}$$