It occurred to me to reverse Archimedes' famous process. Since I know the mass of my pan and can look up the density of stainless steel which varies slightly but is about 7850 kg per cubic metre. That's the same as 7.85 grams per cubic centimetre. Volume = mass/density so the volume of metal in my pan is 1293/7.85 = 164 cubic centimetres. That would be a cube of steel about 5cm on each side - quite a lot.
