In a hydraulic piston set up, one circular piston has a diameter of 2 cm,while the other piston has a diameter of 6cm. Calculate the ratio of the force exerted by the larger piston to the force applied to the smaller piston?

The force ratio is the area ratio, since both pistons experience the same pressure.

To calculate the ratio of the force exerted by the larger piston to the force applied to the smaller piston in a hydraulic system, we need to use Pascal's principle. According to Pascal's principle, the pressure in an enclosed fluid is transmitted equally in all directions.

The formula to calculate the force exerted by a piston is:

Force = Pressure * Area

In the case of a hydraulic system, the pressure is the same throughout the system. Therefore, we can set up an equation using the forces and areas of the pistons:

Force by larger piston / Force applied to smaller piston = Area of larger piston / Area of smaller piston

Let's calculate the areas of the pistons first:

Area of larger piston = π * (radius of larger piston)^2
= π * (diameter of larger piston / 2)^2

Area of smaller piston = π * (radius of smaller piston)^2
= π * (diameter of smaller piston / 2)^2

Given that the diameter of the larger piston is 6 cm and the diameter of the smaller piston is 2 cm, we can calculate the areas as follows:

Area of larger piston = π * (6 cm / 2)^2 = 9π cm^2
Area of smaller piston = π * (2 cm / 2)^2 = π cm^2

Now we can substitute the area values into the equation to find the ratio of the forces:

Force by larger piston / Force applied to smaller piston = (9π cm^2) / (π cm^2) = 9

Therefore, the ratio of the force exerted by the larger piston to the force applied to the smaller piston is 9:1.