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you take the difference because the force due to pressure acting on the top surface has direction upwards, while the force on the bottom surface has the opposite direction (same direction as gravity). So the two forces cancel each other. Becauce the $F_{top}= P_{Ext}\cdot A_{top}$ and $F_{bot}= P_{Ext}\cdot A_{bot}$ the net force is: F_{net}=F_{bot}- F_{...