This question is dependent on two potato variables. The question does provide a fluid volume of 4 cups. The amount of potatoes filing this volume depends on the potato sizes are in which ways they are cut, mashed and or compressed.
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Have you noticed potatoes come in many sizes. Could be anywhere from 6-7 tiny ones to 1 large.
Depends entirely on the size of the potatoes. It could be a half a potato, it could be six potatoes.
You need to know the density of what you are measuring:
Density = MAss of object divided by Volume of object.