The wire bent in the form of square encloses an area of 121 cm2. What is the enclosed area when same wire is bent in the form of circle?
1. 154 cm2
2. 150 cm2
3. 44 cm2
4. 77 cm2
1. 154 cm2
2. 150 cm2
3. 44 cm2
4. 77 cm2
Correct Answer – Option 1 : 154 cm2
Given:
Area of wire bent in the form of square = 121 cm2
Concepts used:
Area of square = (Side)2
The perimeter of wire bent in the form of square = Perimeter of wire bent in the form of the circle
The perimeter of square = 4 × side of the square
Perimeter/Circumference of circle = 2πr
Area of circle = πr2
Where r → Radius
Calculation:
Area of square = (Side)2
⇒ 121 cm2 = (Side)2
⇒ Side = √121 cm
⇒ Side of square = 11 cm
The perimeter of wire bent in the form of square = 4 × side of the square
⇒ 4 × 11 cm
⇒ 44 cm
Let the radius of the circle be r cm.
Perimeter of wire bent in the form of square = Perimeter of wire bent in the form of circle
44 cm = 2πr
⇒ 44 cm = 2 × (22/7) × r
⇒ (44 × 7)/44 cm = r
⇒ r = 7 cm
Area of circle = πr2
⇒ 22/7 × (7)2 cm2
⇒ (22/7) × 49 cm2
⇒ 154 cm2
∴ The wire encloses an area of 154 cm2 when bent in the form of circle.