A wire of 5024 m length is in the form of a square. It is cut and made

1.	A wire of 5024 m length is in the form of a square. It is cut and made a circle. Find the ratio of the area of the square to that of the circle.
Answer» It is given that, Perimeter of the square = 5024 m ⇒ 4 × side = 5024 ⇒ Side = 5024/4 ⇒ Side = 1256 m The same wire is converted into the form of a circle. Therefore, Circumference of the circle = Perimeter of the square ⇒ 2πr = 5024 ⇒ 2 × π × r = 5024 ⇒ r = 2512/π We know that area of the square: Area of the circle = (side)² : πr² Area of square/ area of circle = (side)²/ πr² Area of square/ area of circle = (1256 × 1256)/ [π × (2512/ π) × (2512/ π)] = (1256 × 1256 × 22)/ (2512 × 2512 × 7) = 11/14 Area of the square: Area of the circle = 11: 14

A wire of 5024 m length is in the form of a square. It is cut and made a circle. Find the ratio of the area of the square to that of the circle.

Answer»

It is given that, Perimeter of the square = 5024 m

⇒ 4 × side = 5024

⇒ Side = 5024/4

⇒ Side = 1256 m

The same wire is converted into the form of a circle. Therefore,

Circumference of the circle = Perimeter of the square

⇒ 2πr = 5024

⇒ 2 × π × r = 5024

⇒ r = 2512/π

We know that area of the square: Area of the circle = (side)² : πr²

Area of square/ area of circle = (side)²/ πr²

Area of square/ area of circle = (1256 × 1256)/ [π × (2512/ π) × (2512/ π)]

= (1256 × 1256 × 22)/ (2512 × 2512 × 7)

= 11/14

Area of the square: Area of the circle = 11: 14