Question

Two cylindrical vessels fitted with pistons A and B of area of cross section 8 cm square and 320 cm square respectively , are joined at their bottom by a tube and they are completly filled with water : find (i) the pressure on the piston A (ii) the pressure on piston B (iii) the thrust on piston B

Answer 1

Let E be the effort applied on the smaller piston A and L be the load required on the larger piston B. 
Area of cross section of piston A = 8 cm²
Area of cross section of piston A = 320 cm²
(i) Pressure acting on piston A in the downward direction = Thrust/Area = E/8 cm²
    ∴Pressure acting on water = E/8 cm² (according to Pascal's Law)
(ii) ∴ Pressure acting on piston B =  E/8 cm² (according to Pascal's Law)
(iii) Thrust acting on piston B in the upward direction = Pressure x Area of B
                                                                                    = E x 320 cm²/8 cm²
                                                                                    = 40E  
If E is known you can calculate this.

Answer 2

The diagram is missing here. In the diagram the arrangement would be clearer.

The pistons are exposed to the atmosphere. So atmospheric pressure acts on them.  It is equal to 1.013 * 10⁵ Pa or N/m²  or  1.013 * 10 dynes/cm² 

   As the pistons are both in static equilibrium, the pressure from the water is equal to the atmospheric pressure. So pistons are balanced.  We assume that the pistons are weightless. (otherwise we need to add their weight to the pressure/thrust).

  As the two cylindrical vessels are connected, water flows between them to equalize pressure at the same height or altitude.  Thrust force is the force acting on the piston perpendicular to the surface area.

Pressure by water on Piston A or piston B = 10.13 dynes/cm²

Thrust force
   = pressure * area of cross section
   = 10.13 * 8 =  81.04 dynes  for Piston A
 and 
   = 10.13 * 320 = 3, 241.60 dynes  for piston B
                    (1 dyne = 10⁻⁵ N)