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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 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.

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.

Grade:11

4 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
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
boss
11 Points
8 years ago
Thats exactly whats in the hcv pdf solution. We expect faculties to give their own solution. Who wil join such classes which have such faculties
Sanjeev Srivastava
27 Points
5 years ago
We can visualize the melting of ice in three stages. 
Stage 1 :  Ice = m Water = 0
Stage 2 : Ice = m-x Water = x (Ice still on surface) 
Stage 3 : Ice = m-x' Water = x' (Ice floating on surface)
Now,  In the question it is asked to find the edge length at time it just leaves the contact(last moment of stage 2).  Therefore, we will study stage 2 rather than stage 3.
Follow the HCV Solution. I hope you understand it now.  :)
(Volume dispersed by the block = x²h . density of water) = (Volume of the block at time t)
Ta
13 Points
4 years ago
Let volume of water melted be 64-x³(x is edge length of ice after being melted).
And volume of ice =x³
Now net volume =π*9*x(since radius =3cm )
Now,(64-x³)+x³=9πx
=>x=64/9π=2.26cm.

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