Usually, oil floats on top of water :).

It is true that the pressure exerted by the water exerts a downward force on the sphere. But the water indirectly pushes upward on the sphere as well: the fact that it's there increases the pressure in the oil, so the pressure, and therefore the force exerted by the oil is greater than it would be if the water wasn't there.

Archimedes' principle allows you to skip thinking about the actual pressure on the surface of the sphere that is the origin of the buoyancy force: the total buoyancy is just equal to the weight of the fluid displaced.

So if you were imagine the oil-water interface extending through the sphere (the way it would be if the sphere wasn't there) and then calculate the total weight of the water that it would take to fill the part of the sphere above this surface, and that of the oil it would take to fill the part below it, that's your total buoyancy.

Usually, oil floats on top of water :).

It is true that the pressure exerted by the water exerts a downward force on the sphere. But the water indirectly pushes upward on the sphere as well: the fact that it's there increases the pressure in the oil, so the force exerted by the oil is greater than it would be if the water wasn't there.

Archimedes' principle allows you to skip thinking about the actual pressure on the surface of the sphere that is the origin of the buoyancy force: the total buoyancy is just equal to the weight of the fluid displaced.

So if you were imagine the oil-water interface extending through the sphere (the way it would be if the sphere wasn't there) and then calculate the total weight of the water that it would take to fill the part of the sphere above this surface, and that of the oil it would take to fill the part below it, that's your total buoyancy.

Usually, oil floats on top of water :).

It is true that the pressure exerted by the water exerts a downward force on the sphere. But the water indirectly pushes upward on the sphere as well: the fact that it's there increases the pressure in the oil, so the pressure, and therefore the force, exerted by the oil is greater than it would be if the water wasn't there. Archimedes' principle allows you to skip thinking about the actual pressure on the surface of the sphere that is the origin of the buoyancy force: the total buoyancy is just equal to the weight of the fluid displaced. So if you were imagine the oil-water interface extending through the sphere (the way it would be if the sphere wasn't there) and then calculate the total weight of the water that it would take to fill the part of the sphere above this surface, and that of the oil it would take to fill the part below it, that's your total buoyancy.

Usually, oil floats on top of water :).

It is true that the pressure exerted by the water exerts a downward force on the sphere. But the water indirectly pushes upward on the sphere as well: the fact that it's there increases the pressure in the oil, so the pressure, and therefore the force exerted by the oil is greater than it would be if the water wasn't there.

Archimedes' principle allows you to skip thinking about the actual pressure on the surface of the sphere that is the origin of the buoyancy force: the total buoyancy is just equal to the weight of the fluid displaced.

So if you were imagine the oil-water interface extending through the sphere (the way it would be if the sphere wasn't there) and then calculate the total weight of the water that it would take to fill the part of the sphere above this surface, and that of the oil it would take to fill the part below it, that's your total buoyancy.