Question

if a wire of 440m length is moulded in the form of a circle and a square turn-by-turn, find the ratio of the area of the circle to that of question.​

Answer 1

Answer:

14 : 11

Step-by-step explanation:Total length would not change.  

When formed a circle:

total length = circumference(circle)

⇒ 440 = 2πr          [r = radius]

⇒ 440 = 2(22/7)r

⇒ 70 = r

Area of circle = πr² = (22/7)*(70)²

                       = 15400 m²

When formed a square:

total length = perimeter(square)

⇒ 440 = 4*a             [a=side]

⇒ 110 = s

Area of square = a² = (110)²

                         = 12100 m²

∴ Ratio(area) = 15400/12100

                      = 154/121

                      = 14/11

Answer 2

$\color{blue} \bf \: Given:-$

The Perimeter of Square is 440m

The Circumference of Circle is 440m

$\color{red} \bf \: To \: Find:-$

The Ratio of Their Areas.

$\color{green} \bf \: Solution:-$

The Perimeter of Square = 440m

4 × Side = 440m

Side = 440m/4

Side of Square = 110m

The Area of Square = Side × Side

The Area of Square = 110m × 110m

The Area of Square = 12100m²

The Circumference of Circle = 440m

2 × π × Radius = 440m

2 × 22/7 × Radius = 440m

44/7 × Radius = 440m

Radius = 440m × 7/44

Radius of Circle = 70m

The Area of Circle = π × (Radius)²

The Area of Circle = 22/7 × (70m)²

The Area of Circle = 22/7 × 70m × 70m

The Area of Circle = 15400m²

The Ratio of Their Areas = 15400m²/12100m²

The Ratio of Their Areas = 14/11

The Ratio of Their Areas = 14 : 11

$\color{orange} \bf \: Final \: answer:-$

• The Ratio of Their Areas = 14 : 11

$\color{pink} \bf \:@MrsGoodGirl$