Hi all, I am so confused by the famous Archimedes's story of telling if the crown is made of pure gold. As far as I understand from information posted in the internet, such as http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html Archimedes first determines the volume of the crown by measuring the apparent mass when the crown is immersed into water by a mass spring for example. Then the difference between the actual mass and the apparent mass will be the buoyant force, which is given by the volume of the crown * density of water. From this, we know the volume of the crown. And we can divide the actual mas of the crown by the density of water to get the density of the crown. But can't one just measure the volume of the water displaced when the crown is immersed into the water, and that should be equal to the volume of the crown? Can we get the volume of the crown that way?