Question

A copper wire when bent in the form of a square enclosed an area of $272.25$ $c{m}^2$. If the same wire is bent into the form of a circle, what will be the area enclosed by the wire ?

• A. $346.5$ $c{m}^2$
• B. $364.5$ $c{m}^2$
• C. $356.4$ $c{m}^2$
• D. $463.5$ $c{m}^2$

Answer 1

The correct option is A $346.5$ $c{m}^2$

Area of the square $=272.25c{m}^2$
Let $a$ be the side of the square.
Thus, $a^2=272.25$
$=>a=\sqrt{272.25}$
$=>a=16.5$ cm
Length of the wire is same, thus
Perimeter of the square= circumference of the circle
$=>4a=2\pi r$
$=>r=\frac{2a\times 7}{22}$
$=>r=\frac{2\times 16.5\times 7}{22}$
$=>r=10.5cm$
Now area of the circle $=\pi r^2$
$=\frac{22}{7}(10.5{)}^2$
$=346.5c{m}^2$