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.

Cube   Height
 1        0.48 cm
 2        0.6 cm
 3        0.8 cm
 4        1.066 cm
 5        1.233 cm
 6        1.4 cm
 7        1.48 cm
 8        1.6 cm
 9        1.8 cm
10       2.0 cm with overflow of 0.4 cm³
11       2.0 cm with overflow of 1.0 cm³
12        0* cm with overflow of 1.0 cm³

*The height of the water in the tin, not outside of it.

As the sixth cube could not actually displace the water, assuming, as given that the cubes fit together tightly leaving no spaces, the sixth cube would begin the second layer, raising the height of the remaining 1.4 cm³ water as follows:
 6        1.28 cm
 7        1.35 cm
 8        1.466 cm
 9        1.7 cm 
10       2.0 cm with overflow of 0.4 cm³

Posted by Dej Mar on 2006-05-17 01:58:28