A cylinder contains 0.1 cubic meters of gas at atmospheric pressure. This gas is allowed to expand until its pressure drops to 7800 Pa. What is the gas volume after this expansion has taken place?

Does the temperature stay the same? Or is this an isentropic (adiabatic) expansion? They need to tell you.

All you know is that pressure is decreased by a factor
R2/P1 = 7800/10130 = 0.770

If the process is adiabatic, they need to tell you what the gas is. (The "gamma" specific heat ratio is needed)