Final answer:
All the blocks have the same volume in common. Their differences in mass and density dictate whether they sink or float, with density being the ratio of mass to volume.
Step-by-step explanation:
The property that all the blocks have in common when they displace the same amount of water is that they have the same volume. When submerged, a block of any material will displace a volume of water equal to its own volume. For blocks of the same volume, if they are of different materials, they will have different masses and densities. Density is defined as the mass per unit volume (density = mass/volume). So, for the same volume, the block with the higher density will have a greater mass. This is why, in the question's referenced figures, a block of brass sinks while a block of wood floats. The brass has a higher density than water and thus sinks, whereas the wood has a lower density and floats. Using experimental determination of density, such as the water displacement method, one can find the mass of the displaced water by using the relationship between its volume and density. For example, if the water displaced is 29.5 mL and the density of water is 1.00 g/mL, the mass of water displaced is 29.5 g since mass = volume × density.