krisraam wrote:2 parts of the 6 parts is not painted. so 33 1/3 %.
When you cut the cube, you no long have 6 equal faces, you now have 12 faces (6 on each rectangular solid) and 2 of those faces are not painted, but it is not 2/12, because the faces are no longer equal either - 2 faces are squares of size = s, like the original cube, but the other faces have all been cut in half, so the surface area of these rectangular faces is s^2/2 and there are 8 of these in the new cubes.
So, 2s^2 is the combined surface area of the two non-painted faces that were exposed when the cube was cut.
2s^2 are the painted full sides from the original cube.
8 * (s^2/2) are the 8 rectangular painted surfaces generated by cutting the cube.
So you are looking for 2s^2 / (4s^2) + (8 * (s^s/2)) to find the ratio of all the sides for both rectangular solids.
However, since the cube was cut perfectly in half (which we know since it resulted in rectangular solids of equal volume), you can just look at one rectangular solid and get s^2 / 2s^2 + (4*(s^2/2) which =
s^2/4s^2 = 1/4 = 25%
My question to the original poster is what is OA, since just about everyone is getting 25%, which you said is not OA.
-Carrie
This is really very pathetic elucidation to the problem.
