Question

A wire bent in the shape of a square
with side 11cm was straightened out
and bent in the shape of a circle. Find the radius and area convered by the circle​

Answer 1

Given :

• A wire bent in the shape of a square with side 11cm was straightened out and bent in the shape of a circle

To find :

• Radius and area covered by the circle

Knowledge required :-

→ Formula of perimeter of square :-

• Perimeter of square = 4 × side

→ Formula of Circumference of circle :-

• Circumference = 2πr

→ Formula of area of circle :-

• Area of circle = πr²

where,

• Take π = 22/7
• r = radius of he circle

Solution :

Perimeter of the square :-

⠀⠀⠀⇒ Perimeter = 4 × 11

⠀⠀⠀⇒ Perimeter = 44

Periemter of square = 44 cm

Periemter of the square = Circumference of the circle

So, circumference of circle = 44 cm

⠀⠀⠀⇒ Circumference = 2πr

⠀⠀⠀⇒ 44 = 2 × 22/7 × r

⠀⠀⠀⇒ 44 = 44/7 × r

⠀⠀⠀⇒ 44 × 7/44 = r

⠀⠀⠀⇒ 7 = r

Radius of the circle = 7 cm

Area of circle :-

⠀⠀⠀⇒ Area = πr²

⠀⠀⠀⇒ Area = 22/7 × 7 × 7

⠀⠀⠀⇒ Area = 22 × 7

⠀⠀⠀⇒ Area = 154

Area of the circle = 154 cm²