Two methods were described for determining the volume of the flask used for the molar mass determination. which method will give a more precise determination of the volume.

Precision depends on the ability of the method to reproduce the same or similar result in a measurement.  The methods that after several measurements of the same observation produced the closest values between them is going to be the more precise. 
Ej:
Method A: 3.0 L, 3.1L, 2.9L
Method B: 3.0 L, 4.1L, 1.9L
Method A will be more precise than Method B

Sorry i don’t know answer to this