IBPS SO Prelims Exam Model Paper 4

Given:
The perimeter of square = Perimeter of a semicircle
The perimeter of square + Perimeter of semicircle = 72 cm
Formula used:
The perimeter of square = 4 × side
Perimeter of semicircle = πr + 2r
Area of square = side × sideArea of semicircle =

πr2

2

Calculation:
The sum of the perimeter of circle and square is 72 cm
Suppose the side of the square = x cm
Radius of semicircle = r cm
⇒ 4x = (πr + 2r)
⇒ 4x = (

22r

7

+ 2r)
⇒ 4x =

36r

7

⇒ x =

9r

7

So, 4x + (πr + 2r) = 72
⇒ 4x +

36r

7

= 72
⇒

36r

7

+

36r

7

= 72
⇒ r = 7 cm
And, x = 9 cm
So, Area of the square (9 × 9) = 81 sq. cm
Area of semicircle =

π(7×7)

2

⇒ 77
∴ required ratio = 77 : 81