A cube of ice of edge 4 cm is placed in an empty cylindrical glass of inner diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length (in cm ) of the edge of the ice cube at the instant it just leaves the contact with the bottom of the glass.

Let size of ice block remaining is x3 .When it is just about to  float, then ​∴ x3×ρice g=x2yρwg.....i​⇒ x3ρice =x2yρw​ Also mass of ice melt = mass of water forms ​43−x3×ρice=π×32×y−x2yρw​ or 43ρice −x3ρice =π×32yρw−x2yρw​ or  43ρice =π×32yρw​or    y=7.11ρice πρwSubstituting the value of y in equation (i), we get ​x3×ρice g=x2×7.11ρice πρwρwg​ or  x=2.26cm.