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.
(In reply to this should be the solution
"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"
For 6 times the new height to equal the volume of the water plus the volume of the cube, the cube could not extend above the height of the water--it must be the same 0.5666... cm. But it can't be: it's solid and 1-cm high.
Posted by Charlie
on 2006-05-16 10:46:31