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Cubes in a tin (Posted on 2006-05-15) Difficulty: 2 of 5
There is a rectangular tin 2cm by 3cm at the base, 2cm deep and open at the top.
It is filled with water to a depth of .4cm.
Twelve 1cm steel cubes are placed in the tin one by one. The first six form a single layer at the bottom. The next six form a second layer.

To what height does the water level rise after the placement of each cube?
Assume the cubes fit together tightly, leaving no spaces.

See The Solution Submitted by Jer    
Rating: 2.6667 (6 votes)

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Solution this should be the solution | Comment 7 of 24 |

the volume is 0.4*3*2=2.4cm³

one cube is one cm³ added

so the new volume is after 1cube is 3.4cm³ (2.4cm³+1cm³)

divide this by 6 and you have the new height after one cube = 0.5666...cm

after 2 its 0.7333...cm ((2+2.4)/6)

after 3 its 0.9cm

after 4 its 1.0666...cm

after 5 its 1.2333...cm

after 6 its 1.4cm (easy, cause the six cubes took exactly 1cm of the height, so 1cm filled with cubes, plus 0.4 by the water)

after 7 its 1.5666...cm

after 8 its 1.7333...cm

after 9 its 1.9cm

after 10 its full (0.4cm³ of water has left the cube)

after 11 its full (1cm³ of water left, the volume of the 12th cube)

after 12 the tin is filled with cubes, all the water is gone


  Posted by dominique on 2006-05-16 09:13:59
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