A solid cube of ice of side 30cm is floating in sea water such that 4cm of its height projects above the water surface. The density of ice is 900kgm−3.
(i) Show that, for a floating body, the fraction of its volume submerged in a liquid is equal to the ratio of the density of the body to that of the liquid.
(ii) Using the data given, calculate the density of the sea water.
(iii) If the same ice cube were placed in pure (fresh) water, calculate the height of the cube that would project above the water surface.