Question

7. If a wire of 440 m length is moulded in the form of a circle and a square
find the ratio of the area of the circle to that of square.​

Answer 1

Answer:

14 : 11

Step-by-step explanation:

When it's moulded to a circle (of radius "R")

Length of wire = Circumference of circle

440 m = 2πR

R = 440/(2π) m

R = 220/π m

R = 220/(22/7) m

R = 7 × 220/22 m

R = 7 × 10 m

R = 70 m

Area of circle = πR²

= 22/7 × (70 m)²

= 22/7 × 4900 m²

= 15400 m²

When it's moulded into a square (of side length "a")

Length of wire = Perimeter of square

440 m = 4a

a = 440/4 m

a = 110 m

Area of square

A = a²

= (110 m)²

= 12100 m²

Ratio:

Area of circle / Area of square

= 15400 m² / (12100 m²)

= (14 × 1100 m²) / (11 × 1100 m²)

= 14 / 11

Answer 2

Answer:

14:11

Step-by-step explanation:

Solution:-

Length of wire = 440 m

So, this will be considered as the perimeter for a square and circumference for a circle.

So, according to the question.

Circumference of circle = 2πr

440 = 2*22/7*r

44r = 440*7

r = (440*7)/44

Radius of the circle = 70 m.

Now, area of the circle = πr²

= 22/7*70*7

Area of the circle = 15400 sq m

Now, 

Perimeter of the square = 440 m

Each side of square = Perimeter/4

= 440/4

Each side of square = 110 m

Now,

Area of the square = side × side

= 110 × 110

Area of the square = 12100 sq m

Now,

Ratio of the area of the circle to that the area of the square.

= 15400 : 12100

Ratio = 14 : 11

Answer.