Practically seen, the Archimedes principle allows us to measure the volume of our container, by measuring the volume of the liquid it displaces after the submerging and b) to calculate the buoyancy of an object immersed into a liquid.
We may observe for any immersed object that the volume of the submerged portion equals the volume of fluid it displaces. E.g., by submerging in water half of a sealed 1-liter container, we displace a half-liter volume of fluid, regardless of the container's contents. If we fully submerge the same container, we then displace one liter of liquid, that equals exactly to the volume of the 1-liter container.
If we just take an empty 1-litre plastic bottle in the air and release the bottle, it will fall down due to the gravitational force of Earth acting on our bottle. If we put this bottle under water, there will be still the same gravitational force acting on this bottle. At the same time if we release the bottle it will be pushed upwards towards the surface of the water. This extra force, that pushes our bottle upwards comes from the Upthrust or Archimedes force.
The pressure difference between the bottom and the top face is directly proportional to the height (difference in depth). Multiplying the pressure difference with the area of a face gives the net force on the cube - the buoyancy, or the weight of the fluid displaced. Whatever the shape of the submerged body, the buoyant force is equal to the weight of the fluid displaced.
The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density) the