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 of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.

Sol. Let x → edge of ice block When it just leaves contact with the bottom of the glass. h→ height of water melted from ice W = U ⇒x3 * pice * g = x2 * h * pw * g Again, volume of water formed, from melting of ice is given by, 43 – x3 = π * r2 * h – x2h ( because amount of water = (πr2 – x2)h) ⇒43 – x3 = π * 32 * h – x2h Putting h = 0.9 x ⇒x = 2.26 cm