Well, that's how my little sister asked it, and I couldn't provide a quick answer.
If we ignore any changes in shape from the cutting process, then my first thought was that the scaling wouldn't make any difference. But then I started thinking that more efficient packings might only become possible after we cut the apple pieces down to a certain size.
I realise this is almost unanswerable without multiple assumptions (spherical pieces of apple anyone? :) ) but at the end of the day I'm interested in what is known (if anything) about the packing of irregularly shaped solids in finite containers of similar dimension (within an order of magnitude) to the solids themselves.