What is the total force exerted on a piston that is 5 inches in diameter and operates at a pressure of 125 psi?

To find the total force exerted on a piston, we can use the relationship between pressure, area, and force. The formula is:

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

First, we need to calculate the area of the piston. The area ( A ) of a circle is calculated using the formula:

[ A = \pi r^2 ]

Since the diameter of the piston is given as 5 inches, the radius ( r ) is half of that:

[ r = \frac{5 \text{ inches}}{2} = 2.5 \text{ inches} ]

Now, substituting this radius into the area formula:

[ A = \pi (2.5 \text{ inches})^2 = \pi (6.25) \text{ inches}^2 \approx 19.63 \text{ inches}^2 ]

Next, we convert the pressure from psi to pounds per square inch. The pressure is provided as 125 psi.

Now we can calculate the force:

[ \text{Force} = 125 \text{ psi} \times 19.63 \text{ inches}^