Question

A iron rod is in the form of a square enclosing an area of $22{cm}^2$. If the same iron rod is bent into a circle, then find the area of that circle?

• A. $24{cm}^2$
• B. $26{cm}^2$
• C. $28{cm}^2$
• D. $30{cm}^2$

Answer 1

Answer: (C)

$28{cm}^2$

REF.Image.

Let the length of the wire 'L'

Now, It is bent in the term of square

Hence, L = 4a

Given, $a^2=22$

$\therefore a=\sqrt{22}$

$\therefore L=4\sqrt{22}$

Now, It is bent in the term of circle

$2\pi r=4\sqrt{22}$

$r=\frac{2}{\pi }\sqrt{22}$

$\therefore$ Area of circle = $\pi r^2$

$=\pi \times \frac{4}{\pi 2}\times 22=\frac{4}{\pi }\times 22$

$=\frac{4}{\frac{22}{7}}\times 22=28$

$\therefore A=28c{m}^2$