1. The problem statement, all variables and given/known data

Can somebody please tell me exactly what archimedes prnciple is?

2. Relevant equations

3. The attempt at a solution

So, I watched this video: . Apparently if we have a cube in a bucket of water then the mass of the whole cube is equal to the mass of the displaced water. So that means if the cube and the water has the same mass (and obviously the have different density) then the volume of the displaced water is equal to the volue of the cube that is under the water.

The statement of Arch.P. in the video is correct.
The buoyant force is equal to the weight of liquid displaced.
The volume of liquid displaced is equal to the volume of the submerged part of the object.
The mass of liquid displaced is equal to the volume x density.
The weight of liquid displaced (and hence the buoyant force) is equal to the mass x g.

If buoyant force is greater than the weight of the object, it floats.
If buoyant force is less than weight of object, it sinks.

Is t because the cube and the displaced water have the same volume but if the cube sinks then it has higher density. so with the same volume and higher density then the mass needs to be higher

The amount of water displaced is equal to the volume of block underwater.

When the block floats, the part underwater is displacing water and the mass displaced is equal to the mass of the whole block.

When the block sinks, the whole block is displacing water, but the mass of water displaced is less than the mass of the block. So the buoyant force on the block is less than the force of gravity on the block and it sinks.

The important point to remember is, the upward force is equal to the weight of water displaced. And the amount of water displaced is the volume of block under water.