Answer:
Pressure = Force / Area
Assuming you have created a force by hanging a certain mass from one hemisphere then
Force = Mass * Gravity
We need to consider the area on which the air pressure is acting upwards and supporting the mass. We could look at all of the vectors acting inwards on the lower half of the sphere, but this can be resolved to the same pressure acting upwards over the area across the centre of the sphere - so we take the area as the Cross Sectional Area across the join.
Area = PI * radius^2
So to calculate the pressure use:
Pressure = (Mass*Gravity) / (PI * radius^2)