The diameter of the large cylinder of the hydraulic machine is 50 cm and the diameter

The diameter of the large cylinder of the hydraulic machine is 50 cm and the diameter of the small cylinder is 4 cm. What is the power gain of this machine?

Since the fluid pressure is assumed to be the same for two cylinders, the ratio F1 / S1 = F2 / S2 will be valid.
Hence: F1 / F2 = S1 / S2, where S1 is the surface area of the large cylinder, S2 is the surface area of the small cylinder.
For a circle, the area is S = (ΠD ^ 2) / 4.
F1 / F2 = S1 / S2 = ((ΠD1 ^ 2) / 4) / ((ΠD2 ^ 2) / 4), where D1 = 50 cm, D2 = 4 cm.
F1 / F2 = (D1 ^ 2) / (D2 ^ 2) = (50 ^ 2) / (4 ^ 2) = 2500/16 = 156.25.
Answer. The power gain for the hydraulic machine is 156.25.