We will use the volume of sphere equation which states:

V=(4/3)*pi*r^3

Since the diameter is 12 inches, the radius is:

r=d/2= 6 inches

We plug this into the first equation to get:

V=(4/3)*pi*(6^3)

Solving for V, we get:

V=904.78 in^3

This is the volume of air inside.