Question

If the perimeter of circle is equal that of a square , then the ratio of their areas is​

Answer 1

Answer:

Given:

The perimeter of the circle is equal to that of the square.

Formula:

If “r” is the radius of the circle and a” is the side of the square,

1) Perimeter of a circle = 2πr

2) Area of a circle = πr2

3) Perimeter of a square = 4a

4) Area of a square = a2

Calculation:

Let “r” be the radius of the circle and “a” be the side of the square,

According to the question,

The perimeter of the circle is equal to that of the square.

2πr = 4a

⇒ r/a = 4/(2π) = 2/π ----(1)

Now, the ratio of the area of circle and Area of square:

⇒ πr2/a2 ----(2)

From equation (1) and (2),

πr2/a2 = π(2/π)2

⇒ πr2/a2 = 4/π

∴ The ratio of the area of a circle to that of a square is 4 ∶ π.