Because the cork is lighter than the same bulk of water; hence, it ascends to the surface.
Why does heated air ascend?
Because it is lighter than the cold air.
If a feather be put in the heated air, will it be carried up with the air?
The feather will be carried up with the air.
If warm air be confined in a bag, will it rise up and carry the bag with it?
It will rise up and carry the bag with it.
What might this bag be called?
It might be called a balloon.
What is a balloon?