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.
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
this should be the solution
