Assuming that the gas acts like an ideal gas, we can calculate for the final volume using the ideal gas law:
PV = nRT
Where P = pressure, V = volume, n = number of moles, R = gas constant, and T = temperature
Assuming that P, n, and R are constant throughout the process, we can define another constant K:
V / T = K where K = nR / P
Equating the initial and final states:
Vi / Ti = Vf / Tf
Substituting the given values:
11.5 cm^3 / 415 K = Vf / 200 K
Vf = 5.54 cm^3