bore X bore X stroke X #of cylinders X .7854 = CID
4.060 X 4.060 X 3.48 X 8 X .7854 = 360.42274
That formula actually makes it come out ever so slightly bigger than it really is.
Cylindrical displacement is actually pi x r^2 x h, or in piston engine terms it's pi x (bore / 2)^2 x stroke. The above formula uses bore^2 instead of r^2, which then creates a divisor of 4, and the .7854 constant comes from pi / 4. But that's a rounded figure, the real answer is .78539816, and they rounded up, so the result comes out little bigger than the motor really is. But not much ...
3.1415926539 x 2.030^2 x 3.48 x 8 = 360.4219ci
That's probably inside the resolution of the measuring tools. A .001 error in the bore size measurement makes a bigger difference, and I don't think there's any torque plates in place when the measurement is made in impound so there could easily be that much error. So this slight inaccuracy probably doesn't matter.
If I remember right (no rule book in front of me), the formula the bike guys use for ci to cc has a constant that's even farther off, and it actually could come into play. They should be using 2.54^3, that's an exact conversion factor with no error. What does it say in the bike rules?