Balloon inflation is more complex. If you model it as a sphere, the internal volume goes up as the cube of the radius.
But it makes a huge difference what it's inflated with: air, which is compressible and about follows the ideal gas laws, or water, which is incompressible. The actual inflated diameter depends on the volume of air pumped in, the elasticity of the material, and the external pressure surrounding the balloon, at least.
If you are retaining an enema with a air filled balloon catheter and bear down hard, the balloon will decrease in size and may pop out. I think that's why several bowel catheters, like Instaflo, Actiflow and Flexi-Seal as well as bowel irrigation systems like the Coloclean use water filled balloons.
BTW, nobody has yet answered why water is used in Foley urethral catheters. The reason is not the same.
Water is used for both rectal and urethral Foley catheters. A calibrated syringe only makes any sense to fill a Foley with water, because the size of the balloon is then known.
Also, there are a number rectal nozzles, single use, for Barium enemas. The often use disposable inflators of a plastic soft foam filled plastic bag. One squeeze would inflate the retention balloon to the appropriate size.