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This subatomic particle's mass is 1.672621637(83)×10−27 kg.
That being said, I interpret the question to be asking about volume, rather than mass. There are approximately 4.245e32 protons in a cubic meter of tungsten, which means that a proton must be at most 2,356 cubic picometers in diameter. It's actually much smaller than this, since solid matter is mostly empty at the subatomic level, and not made of a continuous series of protons.