The shaded circles having diameter of 1, 0.5, 0.25 and 0.125 cm are inside squares of side 1 cm as shown in the figure. The ratio of shaded area in A and B is one.

The ratio of shaded area in C and D would be

Correct option is A

Solution:

​In square D, there are 2 circles of diameter 0.5, 4 circles of diameter 0.25 and 16 circles of diameter 0.125.
∴ 

​$$\text{Shaded area of C} \\= \pi \left( \frac{1}{2} \right)^2 \\= \frac{\pi}{4} \\[10pt]\text{Shaded area of D} \\= 2 \times \pi \left( \frac{0.5}{2} \right)^2 + 4 \times \pi \left( \frac{0.25}{2} \right)^2 + 16 \times \pi \left( \frac{0.125}{2} \right)^2 \\= \frac{\pi}{4} \\[10pt]\text{Ratio of shaded area} = \frac{\pi/4}{\pi/4} = 1$$

∴ The ratio of shaded area in C and D would be 1.

If any square plane is covered by a single circle or by n different circles, in both cases the shaded area will be same.

​​