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?