Question

By bending a wire, a square is, made whose area is $x$ sq. units. If a circle is made from same wire, what will be its area?

• A. $\frac{11x}{14}$sq.unit
• B. $\frac{12x}{11}$sq.unit
• C. $\frac{14x}{11}$sq.unit
• D. $\frac{11x}{12}$sq.unit

Answer 1

The correct option is C $\frac{14x}{11}$sq.unit

Area of the square $=x$ sq. units

Let the side be $a$
Area of the square $=a^2=x$
$\therefore x=a^2$ ....(i)

Perimeter of square $=4a$ units

If a circle is made with the same wire then its circumference is equal to the perimeter of the square.
Circumference of the circle $=2\pi r$

$\therefore 2\pi r=4a$
$\Rightarrow \pi r=2a$
$\Rightarrow r=\frac{2}{\pi }a$
Area of the circle

$=\pi r^2$
$=\pi {\left(\frac{2a}{\pi }\right)}^2$ $=\frac{4a^2}{\pi }$
$=\frac{2a^2}{\pi }$$=\frac{7}{22}\times 4a^2$

$=\frac{2a^2}{\pi }$$=\frac{14a^2}{11}$
$=\frac{14x}{11}$
Area of the circle $=\frac{14x}{11}$ sq units.