Aforce of 250n is applied to a hydraulic jack piston wth
a0.1m diameter. if the output piston, which supports the load, has a
diameter of .5m, how much weight can be lifted?

To solve this problem we will apply the Pascal principle. This law establishes that the pressure exerted on an incompressible fluid and in equilibrium within a container of non-deformable walls is transmitted with equal intensity in all directions and at all points of the fluid.

Mathematically the relationship is given as

Since it is a circular piston the area will be given as

Replacing,

Our values are given as

Replacing we have that

Therefore the wieght that can be lifted is 6250N

it has to be b, about 97 percent.