Question

A copper wire when bent in the form of a square encloses an area of 484 cm². 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 cm²
Area of the square = Side² 

⇒ 484 = Side² 

⇒ 22² = Side²

⇒ Side = 22 cm

Perimeter of the square = 4 × Side

Perimeter of the square = 4 × 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:

2πr = 88

`⇒ 2xx22/7xx"r"=88`

⇒ r = 14

Area of the circle = πr² 

`=22/7xx14xx14` 

= 616 cm² 

Thus, the area enclosed by the circle is 616 cm².