Splitting aerosols

How much more surface area do you obtain from splitting aerosols in half? That is to say a constant volume holds while splitting the aerosol volume like so:

I want to compare surface S₁ with surface S₂. Since surface is related to volume like so,

then the ration S₂/S₁ becomes (and accounting for the two spheres in S₂),

Hence there is 26% more surface area available if all sphere of volume V divide into spheres of volume V/2.

If the aerosol is split unevenly into fractions x and 1- x (where 0 < x < 1), then

which looks like this:

The equation is if course symmetric about the point x = 0.5.