A wire in the form of a circle of radius 7 cm is bent to form of square. Find the length of the diagonal of the square.

(Take π = $$\frac{22}{7}$$​)​

Correct option is C

Given:

The wire is initially in the form of a circle with a radius of 7 cm.

The wire is then bent to form a square.

We are asked to find the length of the diagonal of the square.

We are given that $$\pi = \frac{22}{7}.$$​​

Formula Used:
Circumference of the circle (which is the length of the wire) is equal to the perimeter of the square.

Circumference of the circle = 2πr, where r is the radius of the circle.

Perimeter of the square = 4s, where s is the side length of the square.

The diagonal d of the square is related to the side s, d $$= s\sqrt{2}$$​

Solution:

We can equate the circumference of the circle to the perimeter of the square:

2πr = 4s

The radius r = 7 cm, so the circumference of the circle is:

C = $$2 \times \frac{22}{7} \times 7 = 44 \, \text{cm}$$​

This is the length of the wire.
The perimeter of the square is equal to the circumference of the circle, so:

4s = 44

s = $$\frac{44}{4} = 11 \, \text{cm}$$​
The diagonal d of the square is given by:

d =$$s\sqrt{2} = 11\sqrt{2}$$ cm