A cord is in the form of a square enclosing an area of 22 cm². If the same cord is formed into a circle, then find the area enclosed by that circle. [Take π = 22/7]

Correct option is C

Given:

Cord is in the form of a square with an area of $$22 \, \text{cm}^2.$$​​

The same cord is reformed into a circle.

​$$\pi = \frac{22}{7}.$$​​

Solution:

Let the side of the square be s

​$$s = \sqrt{22} \approx 4.6904 \, \text{cm}$$​​

The perimeter (or length of the cord) of the square is:

​$$4s = 4 \times 4.6904 = 18.7616 \, \text{cm}$$​​

Now, form the circle with the same perimeter (circumference):

​$$\text{Circumference} = 2\pi r = 18.76162 \times \frac{22}{7} \times r = \frac{18.7616 \times 7}{2 \times 22} = \frac{131.3312}{44} = 2.984 \, \text{cm}$$​​

The area of the circle:

​$$\text{Area} = \pi r^2 = \frac{22}{7} \times (2.984)^2$$​​

​$$\text{Area} = \frac{22}{7} \times 8.908 \approx 28 \, \text{cm}^2$$​​