A hydraulic jack has an output piston of area 0.100 m2. A 55.8 N input force
creates 419 N of output force. What is
the area of the input piston?

Explanation:

You want the area of the output piston not the input piston.  The input piston creates a pressure equal to  

55.8 N/0.1 m^2  =  558 N/m^2.  This pressure is transmitted through the hydraulic fluid and applied to the output piston.  The pressure exerted on the output piston is equal to 419 N/Am^2.  Set this equal to the applied pressure and solve for A, the area of the output piston.

419/A = 558 ,  A = 419/558 = 0.751 m^2

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