$$0.1$$ percent of $$1.728 \times 10^{6}$$ spherical droplets of water, each of diameter 2 mm, coalesce to form a spherical bubble. What is the diameter (in cm) of the bubble?

$$0.1$$ percent of $$1.728 \times 10^{6}$$

= $$ \frac{0.1}{100} \times 1.728 \times 10^{6} $$

= $$ \frac{1}{1000} \times \frac {1728}{1000} \times 10^{6} $$

= 1728

1728 spherical droplets of water

Diameter = 2mm = 0.2 cm

Radius = 0.2/2 = 0.1 cm

Volume of one Drop = (4/3) π r³ = (4/3) π (0.1)³ cm³

Volume of 1728 spherical droplets of water = 1728 * (4/3) π (0.1)³ = (4/3) π * 1.728 cm³

let us say Diameter of of Spherical Bubble = D cm

Radius = D/2 cm

Volume = (4/3) π (D/2)³ = (4/3) π D³/8 cm³

Equating both volumes:

(4/3) π D³/8 = (4/3) π * 1.728

=> D³ = 8 * 1.728

=> D³ = 2³ * 1.2³

=> D³ = (2 * 1.2)³

=> D = 2.4 cm

Diameter in cm of the spherical bubble = 2.4 cm

option D is correct