Given:
- Diameter of small piston (d1) = 3 cm
- Diameter of large piston (d2) = 10 cm
- Distance between the two pistons (h) = 40 cm
- Force applied on the small piston (F1) = 80 N
- Working fluid is water

To Find:
- Load lifted by the hydraulic jack

Solution:

Step 1: Calculate the areas of the pistons:
- Area of the small piston (A1) = (π/4) x (d1)^2
=> A1 = (π/4) x (3 cm)^2
=> A1 = 7.07 cm²

- Area of the large piston (A2) = (π/4) x (d2)^2
=> A2 = (π/4) x (10 cm)^2
=> A2 = 78.54 cm²

Step 2: Calculate the pressure on the small piston:
- Pressure on the small piston (P1) = Force applied on small piston (F1) / Area of small piston (A1)
=> P1 = 80 N / 7.07 cm²
=> P1 = 11.31 N/cm²

Step 3: Calculate the pressure on the large piston:
- Pressure on the large piston (P2) = Pressure on small piston (P1) x Area of small piston (A1) / Area of large piston (A2)
=> P2 = 11.31 N/cm² x 7.07 cm² / 78.54 cm²
=> P2 = 1.01 N/cm²

Step 4: Calculate the force on the large piston:
- Force on the large piston (F2) = Pressure on large piston (P2) x Area of large piston (A2)
=> F2 = 1.01 N/cm² x 78.54 cm²
=> F2 = 79.99 N

Step 5: Calculate the load lifted:
- The load lifted is equal to the force on the large piston (F2)
=> Load lifted = 79.99 N

Explanation:
- The hydraulic jack works on the principle of Pascal's law, which states that when pressure is applied to a fluid in a confined space, it is transmitted equally in all directions.
- In this case, when a force (F1) is applied to the small piston, it creates a pressure (P1) on the fluid in the system. This pressure is transmitted equally to the larger piston.
- The pressure on the large piston (P2) is calculated using the ratio of the areas of the pistons. This pressure then creates a force (F2) on the large piston, which is equal to the load lifted.
- By using the given values and formulas, we can calculate the load lifted to be 79.99 N.
- It is important to note that the working fluid being water affects the density and properties of the fluid, but it does not significantly impact the calculations in this case.