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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

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.
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. HCV chapter 13 question 25

Grade:12th pass

1 Answers

Rockybhai7009
13 Points
10 months ago
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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