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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 unniformly from each side so that it always retains its cubical shape.Remembering that ice is lighter than water, find the length of edge of the ice cube at the instant it just leaves contact with the bottom of the glas. . . HCV chapter 13 question 25
Here, The volume of the ice dissolved = the volume of water formed let the length of ice converted into water = k => volume of ice dissolved = 4 x 4 x k the volume of water formed will be in the form of 32 x h x 22/7(pi) where h is the height of the water formed. For the ice block to just leave contact with the bottom we need to take h is negligible => 9x22/7(pi) is the minimum amount of water formed so that the ice block just leaves conatact with the bottom. => 9x22/7(pi) = 4x4xk => k = 1.7678571429 Since we need to calculate the height of the ice block remaining Height remaining = initial height – height dissolved = 4 – 1.7678571429 = 2.23215 which is approximately 2.26
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