Question

A copper wire when bent in the form of a square encloses an area of $484$sq.cm. The same wire is not bent in the form of a circle. Find the area enclosed by the circle.

Answer 1

Area of the circle $=484$sq.cm

Area of the square $={\left(Side\right)}^2$

$\Rightarrow 484={\left(Side\right)}^2$

$\Rightarrow {22}^2={\left(Side\right)}^2$

$\Rightarrow$ Side$=22$ cm

Perimeter of the square $=4\times$Side

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

Length of the wire $=88$ cm

Circumference of the circle $=$ Length of the wire $=88$ cm

Now, let the radius of the circle be $r$ cm.

​Thus, we have:

​$2\pi r=88$

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

$\Rightarrow r=\frac{88\times 7}{2\times 22}=14$

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

Thus, the area enclosed by the circle is $616$sq.cm