The air inside the tire exceeds the outside pressure. At sea level, air exerts 14.7 pounds per square inch on all surfaces. This includes the outside of tires as well as the inside. Compressed air is pumped into the tire to say 35 pounds per square inch. Inside the tire has 35 psi being exerted on all surfaces. Remember, 35 pounds per square inch. Calculate the area inside the tire and for every square inch, there is 35 pounds of pressure being exerted on every square inch.
Hydraulics work on the same principals.