The perimeter of a square of side 11 cm is equal to circumference of a circle; then the diameter of the circle is :

1. 7 cm

2. 7.5 cm

3. 14 cm

4. 3.5 cm

Given:

The perimeter of a square = The circumference of a circle

Side of the square = 11 cm

As we know, the perimeter of a square = 4 x side

= 4 x 11 cm

= 44 cm

Let r be the radius of the circle.

And, the circumference of the circle = 2πr

⇒ 2πr = 44

Substitute π = $\dfrac{22}{7}$ :

$⇒ 2 \times \dfrac{22}{7} \times r = 44\\[1em] ⇒ \dfrac{44}{7} \times r = 44\\[1em] ⇒ r = \dfrac{44 \times 7}{44}\\[1em] ⇒ r = \dfrac{\cancel{44} \times 7}{\cancel{44}}\\[1em] ⇒ r = 7 \text{ cm}$

So, the diameter of the circle = 2 x radius

= 2 x 7 cm

= 14 cm

Hence, option 1 is the correct option.