Question

A copper wire is bent in the shape of a square of area 81 cm². If the same wire is bent in the form of a semicircle, the radius (in cm) of the semicircle is \((use \ \pi = \frac{22}{7})\)
1. 7
2. 126
3. 10
4. 14

Answer 1

Correct Answer - Option 1 : 7

Given:

Area of the square = 81 cm2

Formulae Used:

Perimeter (Circumference) of a semi circle = r(π + 2), where r = radius of the circle

Area of the square = a2

Concept Used:

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

 Circumference of the semi circle = Length of the wire

Calculations: 

Side of the square = √(81) cm

⇒ Side of the square = 9 cm

Length of the wire = 4× Length of side

= (4 × 9) cm

= 36 cm

According to question,

⇒ r(π + 2) = 36 where, r = Radius of the circle

⇒ r × (22/7 + 2) = 36

⇒ r × (36/7) = 36

⇒ r = 7

⇒ r = 7 cm

∴ The radius of the semi circle is 7 cm