The circumference of a circle is 100 cm. The side of a square inscribed in the circle is · ABC26GN4629
Subject: General Aptitude · Chapter: Area
The circumference of a circle is 100 cm. The side of a square inscribed in the circle is
(a)$50 \sqrt{2} \mathrm{cm}^{2}$
(b)$\frac{100}{\pi} \mathrm{cm}^{2}$
(c)$\frac{50 \sqrt{2}}{\pi} \mathrm{cm}^{2}$
(d)$\frac{100 \sqrt{2}}{\pi} \mathrm{cm}^{2}$
Answer
Explanation
$2 \pi R=100 \Leftrightarrow R=\frac{100}{2 \pi}=\frac{50}{\pi}$. $$R=\frac{1}{2} \times \text { diagonal } \Leftrightarrow \text { diagonal }=2 R=\frac{2 \times 50}{\pi}=\frac{100}{\pi} .$$ ∴ Area of the square $=\frac{1}{2} \times(\text { diagonal })^{2}=\frac{1}{2} \times\left(\frac{100}{\pi}\right)^{2}$ $$\Leftrightarrow \quad a^{2}=\frac{1}{2} \times\left(\frac{100}{\pi}\right)^{2} \Leftrightarrow a=\frac{1}{\sqrt{2}} \times \frac{100}{\pi}=\frac{50 \sqrt{2}}{\pi} \mathrm{cm} .$$
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