Applying Avagadro's law: the relationship between moles and volume of a gas
You are correct in your approach and answer. Assuming the gas to be ideal, one can apply Avogadro's Law which states that for an ideal gas $V \propto n$.

This implies $V_1/n_1 = V_2/n_2$.

Using the given values one does obtain the volume as $568.75\ \mathrm{mL}$