We take the same three cubes and immerse them, one at a time, in the fluid. The fluid applies a force to each of the six sides of the cube. The force on any side is the pressure times the area. The direction of each force is perpendicular to the side, pointing toward the inside of the cube.

The buoyant force is the vector sum of all these forces.

The force on the left side cancels the force on the right.

The force on the front cancels the force on the back.

Because the pressure at the top is less than the pressure on the bottom, the upward force at the bottom is larger than the downward force on the top. The buoyant force is just the difference between these two forces, so it must equal the pressure difference multiplied by the area of the top (or bottom - they have the same area).

DP = rgh, where h is the distance between the top of the cube and the bottom of the cube. In other words h is the height of the cube.

So, the buoyant force is F_b = DP A = rgh A

What is h * A?

That the volume of the cube. So, now we have that the buoyant force equals:

Lesson 3: F_b = rgV

The density is the density of the fluid. The volume here is the entire volume of the object, but in general it is equal to the volume of fluid displaced by the object.

What happens if we take the cube deeper into the fluid?

All the pressures go up, but the pressure difference between the top and bottom of the object stays the same, so the buoyant force stays the same.

Lesson 4: Changing depth has no effect on the buoyant force applied to a completely submerged object (as long as the fluid density is constant, which is our standard assumption).