As shown in the given figure, inside the large semicircle, three semicircles (with equal radii) are drawn so that their diameters all sit on the large semicircle's diameter. What is the ratio between the white and blue areas?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 1:2
Let the diameter of a big semicircle = 6 unit
the radius of this big semicircle = 6/2 = 3 unit
then the diameter of a small semicircle = 6/3 = 2 unit
the radius of this small semicircle = 2/2 = 1 unit
As we know the area of a semicircle = 2 * π * radius2
The area of the blue section = 2 * π * 9 - 3 * 2 * π * 1 = 12π
According to the question
the ratio between the red and blue areas = 3 * 2 * π * 1/ 12 π = 6/12 = 1/2
Hence, Required ratio = 1: 2