SOLUTION: i need help with this question: One thousand cubes are arranged to form a large cube. All the surfaces of the large cube are painted. What fraction of the cubes are not painted at

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Question 117097: i need help with this question: One thousand cubes are arranged to form a large cube. All the surfaces of the large cube are painted. What fraction of the cubes are not painted at all?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

I need help with this question: One thousand cubes are arranged to form
a large cube. All the surfaces of the large cube are painted. What 
fraction of the cubes are not painted at all?

Since there are 1000 blocks, and since the cube root of 1000 is 10,
the large cube is 10x10x10. If we take away the outer shell of painted 
blocks, the only ones which are painted, there will be a 8x8x8 cube left.
(Remember out of each face we must take off the laft row and and the right
row of blocks, that's why there are 2 less than 10 on each side).

So the answer is 8%5E3%2F10%5E3 = 512%2F1000 = 64%2F125

Edwin