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Grade 12th passIIT JEE Entrance Exam

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

Isha Prabhu

5 Years agoGrade 12th pass

1 Answer

Rockybhai7009

5 Years 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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