Question

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 in the form of a circle.
(Take $\pi$ = $\frac{22}{7}$)

• A. $125$ ${\text{cm}}^2$
• B. $230$ ${\text{cm}}^2$
• C. $550$ ${\text{cm}}^2$
• D. $616$ ${\text{cm}}^2$

Answer 1

The correct option is D $616$ ${\text{cm}}^2$

We have,Area of the square$=a^2=484$ sq.cm

$\therefore$Side of the square$=\sqrt{484}=22$cm

So,Perimeter of the square$=4\times side=4\times 22=88$cm

Let $r$ be the radius of the circle

Then, according to the question,

Circumference of the circle$=$Perimeter of the square.

$\Rightarrow 2\pi r=88$

$\Rightarrow 2\times \frac{22}{7}r=88$

$\Rightarrow r=\frac{88\times 7}{2\times 22}$

$\Rightarrow r=14$cm

$\therefore$Are of the circle$=\pi r^2=\frac{22}{7}\times {14}^2=\frac{22}{7}\times 14\times 14=22\times 2\times 14=616$ sq.cm