Calculate the pressure in kPa, produced by a piston that applies a force of 12 kN, in the oil contained in a closed cylinder. Plunger diameter It is 75mm.

To calculate the pressure produced by the piston, we can use the formula:

P = \frac{F}{A}

where
P is the pressure,
F is the force applied by the piston (12 kN = 12000 N),
and A is the area on which the force is applied.

The area A can be calculated using the formula:

A = \frac{\pi d^2}{4}

where d is the diameter of the plunger (75 mm = 0.075 m).

Substitute the given values:

A = \frac{\pi \cdot 0.075^2}{4}
A = \frac{\pi \cdot 0.005625}{4}
A = \frac{0.01768}{4}
A = 0.00442 m^2

Now, substitute the force F = 12000 N and area A = 0.00442 m^2 into the formula for pressure:

P = \frac{12000}{0.00442}
P = 27165.98\ kPa

Therefore, the pressure produced by the piston is 27165.98\ kPa .

\boxed{P = 27165.98\ kPa}