A Different Kind of Boat

Bengt has a thick metal sheet. It is in the shape of a hexagon with the side 1 m. Now he wants to make it float. Here's his idea:
He will drill a lot of holes in the sheet. Then he will put a very thin metal sheet on each side, so that the air can't escape.
He has drill bits in all sizes. The holes can be infinitely close, but must not overlap. The volume of the thin sheets can be neglected.

1. If he chooses the best possible size of the bit (but only one size), which fraction of the mass of the sheet will remain?
   
2. What if he chooses the worst possible?
   
3. What if he uses the best possible combination of two sizes?
   
4. What if he uses the best possible combination of n sizes?
   
5. How many sizes would he need to make the plan work (get the boat to float on water) if the sheet is made of iron? How about lead? Aluminium?