We're not going to do your homework for you, but here's the general approach.
Archimedes' Principle states that the buoyant force on something
is equal to the weight of the water that is displaced. In some of your
problems you are given a weight which is to be canceled by a buoyant
force and asked to calculate the volume of water displaced, and in
others you are give the volume displaced and asked to calculate the
The sum of the forces on the objects in your problems will be that
of gravity, that of the buoyant force pushing upwards, and any other
forces, like that of the cable suspending your steel cube from the
In your first problem, the volume of water displaced is just the
area of the boat's cross-section times the depth below water the bottom
is. You'll need the density of water to find out how much volume
corresponds to 2000 kg.
The others are just variations on this theme.
(republished on 07/31/06)