a) Calculate the density of the block.
The density of any substance is defined as the mass divided the volume.
Density of the block = mass of the block/volume of the block.
We are given the mass of the block.
mass of the block = 5.60 kg
Since the it is an iron cube, we can find its volume.
Side = 20 cm = 0.20 m
Volume of the block = (side)³
Volume of the block = (20 cm)³ = (0.20 m)³
Volume of the block = 8000 cm³ = 0.008 m³
Now that we know the mass and the volume we can find the density of the block.
Density of the block = Mass of the block / Volume of the block
Density of the block = 5.60 kg / 8000 cm³
Density of the block = 0.0007 kg/cm³
Density of the block = 5.60 kg / 0.008 m³
Density of the block = 700 kg/m³
Answer: The density of the block is 0.0007 kg/cm³ or 700 kg/m³
b) Calculate the mass of water displaced:
If we consider that the cube is completely submerged (as the problem says) it will displace some water. How much water does it displace? Archimedes' says: "The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid". That means that the block completely submerged in water (fluid) will displace its volume of water.
volume of water displaced = volume of the block
volume of water displaced = 8000 cm³ = 0.008 m³
Now that we know the volume of water displaced, and since we are given the density of water, we can find the mass of water displaced.
Density of water = mass of water / volume of water
mass of water = volume of water * density of water
mass of water = 0.008 m³ * 1000 kg/m³
mass of water displaced = 8.0 kg
Answer: Supposing that the block is completely submerged it displaces 8.0 kg of water.