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Force on the upper face of the cylinder = hρgA

Force on the lower face of the cylinder = [h + L]ρgA

Difference in force = LρgA

But LA is the volume of liquid displaced by the cylinder, and LrgA is the weight of the liquid displaced by the cylinder.

Therefore there is a net upward force on the cylinder equal to the weight of the fluid displaced by it.

The same result will be obtained for a body of any shape, regular or not by taking into account the vertical and horirontal components of the forces on the object.

If a sphere of radius r made of material of density σ is fully immersed in a liquid of density ρ the apparent weight of the sphere is given by:

Apparent weight = actual weight - upthrust = 4/3 πr3g(ρ - s)

Mass= Volume×Density

W= V×D

W1-W2=(V1-V2)×D (Density of water =1g/cm³)

=V2-V1×1

=V2-V1

Weight of loss of an object=Weight of water displaced

Archimedes' principle is verified.