One method would be with water displacement.
Fill a graduated cylinder with a known amount of water.
Drop in the nut.
Push below surface with wire, or something with negligible volume.
Read volume, and subtract.
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It is not possible to calculate the area given only the volume.
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You cannot calculate volume of surface area. If you meant 20m3, then the volume would be 20,000 litres.
Not enough information. To calculate mass, you would need volume and density (mass = volume x density).
Bulk density = dry weight / volume, then by knowing the dry weight and bulk density we can calculate the volume.