Question

As shown in the given figure, inside the large semicircle, two semicircles (with equal radii) are drawn so that their diameters all sit on the large semicircle's diameter. What is the ratio between the red and blue areas?

• A. 2 : 3
• B. 2 : 1
• C. 1 : 2
• D. 1 : 1

Answer 1

Answer:

D. 1 : 1

Solution:

Concept used:

Area of semicircle = πr²/2

Here,

r = radius of the circle

Calculation:

Let the radius of the bigger large semicircle be R

So, the diameter of the two small semicircles = R

Now,

Diameter the bigger large semicircle = 2R

So, the area of the larger semicircle = πR²/2

Again,

Total area of two small semicircle = 2 × {π(R/2)²/2}

⇒ πR²/4 i.e red area

So, the area of the blue area = area of the larger semicircle - area of the two small semicircles

The area of the blue area = πR²/2 - πR²/4

⇒ πR2/4

So, ratio = πR²/4 : πR²/4 = 1 : 1

∴ The ratio between the red and blue areas is 1 : 1