ARCHIMEDES' PRINCIPLE

Since the block is unmoving, we know that the forces acting on it are balanced.  Fdown=Fup.
Also remember that density = mass/volume
The force acting downward is the mg of the block, same as (Dblock)(g)(Vblock).
The upward force is from the displaced water, so only acts on part of the block: (Dwater)(g)(Vsubmerged).

Returning to the fact that the forces are balanced... we can use the equality
(Dblock)(g)(Vblock)=(Dwater)(g)(Vsubmerged). and solve for the unknown variable.  Notice that "g" cancels.  Regular platform balances are used to find the mass of the blocks.

Students make a mark on their block and float it in the water.  Works every time.