A hydraulic system for a dentist's chair is designed to be able to lift 3,112 newtons. The surface area over which this force is applied is 707 cm 2. What force must be applied to the activator end of the system if the button has a surface area of 3.14 cm 2

13.8 N

Explanation:

Pressure on the one end of the hydraulic system = Pressure on the other end

Pressure = Force / Area where Force is in Newton, area is in m²

so Force of one end (F1) / area of that end = force of the other end (F2) / area of that end

3112 / (707 / 10000) in m² = F2 / (3.14 / 10000) in m²

cross multiply

44016.97 * 0.000314 = 13.82 N