The Math Equations First of all we have the Titanic when it is a float. This is because we have a mass that is spread out of wide volumes using the equation rho= M/V. Once the ship starts filling up with water the volume displacement of the Titanic becomes smaller making rho increase. When rho (density) of the ship becomes greater than that of water the ship starts to sink.  Lastly from buoyancy equations the density of the whole ship has to be smaller than the total mass for the ship to stay a float.  An example is a empty aluminum can floating on water but once you crush the can or put a hole in it big enough for water to leak in than the can starts to sink or sink immediately.  Link to picture