Question

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(a)13 : 22
(b)14 : 11
(c)22 : 13
(d)11 : 14

Answer 1

Answer:

The ratio of area of circle and square is 14 : 11.

Among the given options option (b) 14 : 11 is the correct answer.

Step-by-step explanation:

Given :

Perimeter of a circle is equal to the perimeter of square.

Let 'r' be the circle of radius and side of a square be ‘a’.

Perimeter of a circle = Perimeter of square.

2πr = 4a

r = 4a/2π

r = 2a/π  

Radius of a circle ,r  = 2a/π  ...............(1)

Ratio of area of circle and area of square  :

Area of circle ,A1 : Area of square,A2

A1 : A2 = πr² : side²

A1 / A2 = π ×(2a/π)² / a²

[From eq 1}

A1 / A2 = π × 4a²/π² / a²

A1 / A2 =  4a²/π  × 1/ a²

A1 / A2 =  4/π  

A1 / A2 =  4/(22/7)

A1 / A2 =  4 × 7/22  

A1 / A2 =  28/22 = 14/11

A1 / A2 = 14/11

A1 : A2 = 14 : 11

Hence, the ratio of area of circle and square is 14 : 11.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution:

Let radius of a circle = r

side of a square = a

According to the problem given,

i) circumference of the circle

= perimeter of the square

=> 2πr = 4a

=> r/a = 4/2π

=> r/a = 2/π ----(1)

ii ) Ratio of areas = (area of the circle)/(area of the square)

= (πr²)/a²

= π(r/a)²

= π ( 2/π)² /* from (1)*/

= π × (4/π²)

= 4/π

= 4/(22/7)

= (4×7)/22

After cancellation, we get

= 14/11

= 14:11

Therefore,

Option (b) is correct.

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