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The cup with the greater volume of water will take longer to cool, as its surface-area to volume ratio is lower, (“area” includes the area in contact with the cup).If you have a thermometer you could perform this experiment and find out which cools faster, e.g. time how long each takes to cool from 90C to 60C. Yes I did notice that the cup diameter increases slightly towards the top,So the water in the fuller cup will have slightly larger area exposed to the air ,But this is negligible compared with the additional thermal inertia of the larger volume of water.
In Newton's Law of Cooling the heat change (ΔQ) is proportional to the mass (m) so it looks as if the larger will cool slower.