Re: Why does acetone dissolve a sytrofoam cup but water will not?

First of all, the "like dissolves like" idea doesn't imply that solvents 
miscible with each other will dissolve the same set of compounds. The 
solubility is a complex phenomenon and all the interactions between the 
molecules must be taken into account before we draw a final conclusion.
Apart from the dipole interactions, there are other types of interactions 
that often play decisive role.
With regard to polarity, the difference between water and acetone is not 
as great as the difference between water and styrofoam. On the other hand, 
with regard to chemical composition and structure, there is similarity 
between acetone and styrofoam. So there is no serious contradiction with 
the "like dissolves like" idea.