Question

A copper wire is bent in the form of a square with an area of 121 cm². If the same wire is bent in the form of a circle, the radius (in cm) of the circle is (Take, π = 22/7 ) :
1. 8
2. 7
3. 12
4. 14

Answer 1

Correct Answer - Option 2 : 7

Given:

Area of the square = 121 cm2

Formulae Used:

Perimeter (Circumference) of a circle = 2πr, where r = radius of the circle

Area of the square = a², a = side of the square

Area of a circle = π(radius)2

Concept Used:

If the same wire is bent in the form of a circle,

Circumference of the circle = Length of the wire

Calculations: 

Side of the square = √(121) cm

⇒ Side of the square = 11 cm

Length of the wire = 4 × Length of side

= (4 × 11) cm

= 44 cm

According to the question,

⇒ 2 × π × r = 44 where, r = Radius of the circle

⇒ 2 × (22/7) × r = 44

⇒ r = (44 × 7)/44

⇒ r = 7 cm

∴ The radius of the circle is 7 cm.