Question 1013080: A cube can be painted completely using 7 litres of paint. Now this cube is cut into 125 identical cubes. How many litres of paint is needed to paint all these small cubes completely with a different colour?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! I like this problem...may ask my own students this one...
Anyway, here's how to look at it...
If you chop a cube up into 125 identical little cubes, there are 5 on each side of the original cube. 125 little cubes have six faces each, or 750 total faces.
Let's say the original cube was painted blue. How many faces were painted blue? How many weren't painted at all?
Well, there are 8 corners, each with 3 painted faces = 24 faces
There are 12 edges, each with 3 cubes with 2 painted faces = 72 faces
There are 9 cubes on each side of the original cube with 1 painted face = 54 faces
So a total of 150 faces were painted. That means 600 have yet to be painted red.
If it took 7 liters to paint 150 faces, it takes 28 liters to paint the remaining 600 faces.
Now if you needed to paint all the faces of all the cubes over again, then the answer is 35 liters.
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