# $$Floating$$ $$Ice$$ $$Cube$$

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.

$$Details$$ $$and$$ $$Assumptions$$

$$Density$$ $$of$$ $$Ice = 900 kg/m^3$$ $$;$$ $$Density$$ $$of$$ $$Water = 1000 kg/m^3$$

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