# Can a small thrust in the horizontal direction generate a large force on the slope?

This is a closed container, which is filled with liquid (blue). We give the piston a horizontal force (red). Will there be a greater force on the slope of the piston? Why? According to Pascal's law, it seems that a greater force will be obtained. But I'm not sure.

Let the sloping part (area A') of the piston be at an angle $$\theta$$ to the end face (area A) of the piston if it were shaped as usual. Then $$A'= \frac{A}{\cos \theta}$$So the force on the sloping part of the piston will be greater than it would be on the end of the piston if shaped as usual, since $$pA'>pA$$ simply because $$A'>A.$$.
The component of this force parallel to the axis of the piston is $$pA' \cos \theta = p \times \frac{A}{\cos \theta} \times \cos \theta =pA$$ So this force component is exactly the same as if the piston were shaped as usual.