For radius x, Choice 'A' π/4 is the correct answer.
For radius 10x, Choice 'B' π/4 is the correct answer.
For radius 100x, Choice 'B' π/4 is the correct answer.
Step-by-step explanation:
The Area of the circle = πr^2, where "r" is the length of the radius.
The Area of square = a^2, where "a" is the length of an edge of a square.
CASE 1 :
Substitute radius r = x and edge length a = 2x,
Area of circle = π*x*x = πx^2
Area of square = 2x*2x = 4x^2
The ratio of the area of the circle to the area of square = πx^2 / 4x^2 = π/4
Choice 'A' π/4 is the correct answer.
CASE 2 :
Substitute radius r = 10x and edge length a = 20x,
Area of circle = π*10x*10x = 100πx^2
Area of square = 20x*20x = 400x^2
Ratio of the area of the circle to the area of square = 100πx^2 / 400x^2
= π/4
Choice 'B' π/4 is the correct answer.
CASE 3 :
Substitute radius r = 100x and edge length a = 200x,
Area of circle = π*100x*100x = 10000πx^2
Area of square = 200x*200x = 40000x^2
Ratio of area of the circle to the area of square = 10000πx^2 / 40000x^2
= π/4
Choice 'B' π/4 is the correct answer.
