I think LRod posted the correct answer in post #11. Below I have reposted his thoughts on this and have added some notes in case the calculated numbers like 3.97899 might actually be 4 in true measure.
Well, the area of the circle describing the cylinder is pi*r^2, so to find r we must first determine the diameter by dividing the circumference by pi :
12.5"/pi = 3.97899" (diameter) (*true measure might be 4")
The radius then is 3.97899/2 = 1.989" (true measure might be 2")
Then we find the area of the circle described by the cylinder as pi * r^2
1.989^2 = 3.958 (
*true measure might be 2 squared = 4)
3.958 * pi = 12.434 in^2 (4 x 3.1416 = 12.5664)
Every linear inch of the length of that cylinder then is 12.434 in^3, so the cylinder volume is 273.555 in^3
If there is an error in the original measurement and the true diameter of the cylinder is 4", then the volume of the cylinder is 22 x 12.5664 = 276.4608 cu. in.