\(Floating\) \(Ice\) \(Cube\)
A cube of ice of edge \(4\) \(cm\) is placed in an empty cylindrical tumbler of inner diameter \(6\) \(cm\). Assume that ice melts uniformly from each side so that it always retains its cubical shape. Find the length of the edge of the ice cube \((in\) \(centimeters)\) at the instant it just leaves contact with the bottom of the glass.
\(Details\) \(and\) \(Assumptions\)
\(Density\) \(of\) \(Ice = 900 kg/m^3\) \(;\) \(Density\) \(of\) \(Water = 1000 kg/m^3\)