In a double actuating cylinder system with 3000 PSI, what is the total force exerted by a piston with a surface area of three square inches on the extension side?

To determine the total force exerted by a piston in a hydraulic system, you can use the formula:

[ \text{Force} = \text{Pressure} \times \text{Area} ]

In this case, the system operates at a pressure of 3000 PSI (pounds per square inch), and the surface area of the piston is three square inches.

Substituting the values into the formula gives:

[ \text{Force} = 3000 , \text{PSI} \times 3 , \text{square inches} = 9000 , \text{pounds} ]

Thus, the total force exerted by the piston on the extension side is 9000 pounds.

B is the correct answer because it correctly applies the principles of hydraulics—specifically, that force is a function of both pressure and area. This relationship illustrates how hydraulic systems can multiply force, which is essential for various mechanical applications.