Max Vehicle Weight for 19.3 atm Hydraulic Lift (23.8 cm Diameter)

[lovelylm1980]

im back again with another problem. The maximum gauge pressure in a hydraulic lift is 19.3 atm. What is the largest size vehicle ( kg) it can lift if the diameter of the output line is 23.8 cm?
What I did was convert 19.3 atm to 1.96e6 N/m^2, then I got density by using the formual P= rho x g x h, my result was a density of 8.40e5 kg/m^3. My goal was to determine the volume and then get mass using m= rho x V. Is this the right way to go about this problem?

 

[HallsofIvy]

I don't see any reason to get that complicated. You already have the pressure in N/m^2 and you know the diameter of the output line is 23.8 cm so the radius is 11.9 cm= 0.119 m. You can calculate the cross section area of the output line which is the area to which the pressure is applied. Multiply the pressure in N/m^2 by the area in m^2 to get the force in N. Since the problem asks for the answer in kg, you will have to divide the force (weight that can be lifted) by 9.81 to get the mass.