50) Four circles of equal radii are centered at the four vertices of a square. These 4 circles touch a fifth circle of
equal radius placed inside this square. The ratio of the shaded area of the circles to the un-shaded area of the
circles is.
A) 5:2
B) 2:3
Ø 3:2
D) 2:5

The ratio of the shaded area of the circles to the un-shaded area of the  circles is 2:3. Option B is correct.

The formula for calculating the area of a circle is expressed as:

A = πr²

Let the area of the shaded part be and the area of the unshaded part be

The area of the shaded part is 2 circles while the area of the total unshaded part is 3 circles.

and

Taking the ratios of the areas

Hence the ratio of the shaded area of the circles to the un-shaded area of the  circles is 2:3

Learn more here: link

B. 2:3

Step-by-step explanation:

It's easier to see when counting by quarters of a circle instead of a whole circle.

We start with the shaded. We know the fully shaded one has 4 quarters and we can count 4 more surrounding it. That's a total of 8. Since there are 4 quarters in each circle, we can divide it by 4 to get 2 full circles that are shaded.

Next is the white, they come in groups of 3 quarters since one of the quarters are shaded. There are 4 groups of these so we can do 3x4 to figure out the total number (or just count them out). We get a total of 12 white quarters. Divide by 4, we have 3 full white circles.

The ratio is 2:3