An ice cube with an edge of 4 cm is placed into an empty cylindrical glass having an inner diameter of 6 cm . The ice melts uniformly from each side, continuously maintaining its cubical shape. Given that ice is lighter than water, determine the length of the edge of the ice cube at the exact instant it just loses contact with the bottom of the glass.

Step-by-step solution

Let the initial edge length of the ice cube be a₀ = 4 cm . Let the edge length of the ice cube at the given instant be a . The inner cross-sectional area of the cylindrical glass is A = r^2 = (3)^2 = 9 cm ^2 . The volume of ice that has melted is a₀^3 - a^3 . The mass of the melted ice is _i (a₀^3 - a^3) , where _i is the density of ice. The volume of water formed from the melted ice is V_w = _i _w (a₀^3 - a^3) , where _w is the density of water. At the instant the ice cube just loses contact with the bottom of the