Diameter of Football Players' Piston: Calculating

[pshla]

Homework Statement

A 55 kg cheerleader uses an oil-filled hydraulic lift to hold four 110 kg football players at a height of 1.0m. If her piston is 16 cm in diameter, what is the diameter of the football players' piston?

Homework Equations

F1/A1=F2/A2
A=pi*r^2
F=mg

The Attempt at a Solution

(55)(9.8)/pi(0.08)^2=(440)(9.8)/pi(r^2)

After I did this, I realized that I need to work the height into the equation, but I'm not sure where it would fit in.

 

[mgb_phys]

The simplest way is to think of the volume displaced - since the hydraulic fluid is in incompressible that must be the same for the cheerleader and the footballers.
In addition the force exerted by the cheerleader and footballers is known.

area_cheerleader * height_cheer = area_footballers * height_footballers
55g / area_chearleader = 110g/area_footballer

The unknowns are area_footballer and height_cheerleader.