SOLUTION: Imagine 1000 blocks, each 1.0 cm on each side stacked in two possible ways. First, consider all blocks stacked in a single cube 10. cm on a side, and second, divided into eight

Question 1096048: Imagine 1000 blocks, each 1.0 cm on each side stacked in two possible ways.
First, consider all blocks stacked in a single cube 10. cm on a side, and second, divided into eight cubes, each of them 5.0 cm on a side.
What percentage of the blocks has at least one face exposed in the first manner of stacking, and what percentage of the blocks has at least one face exposed in the second?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

When the cubes are stacked in the first manner, forming a 10x10x10 cube, the cubes that do NOT have a face painted form an 8x8x8 cube. So there are 512 small cubes with no face painted, which means there are 1000-512 = 488 small cubes with at least on face painted.

488/1000= 48.8%

When the cubes are stacked in the second manner, forming eight cubes each 5x5x5, the small cubes in each 5x5x5 cube with no face painted form a 3x3x3 cube. So in each of the 8 cubes made up of 125 small cubes, there are 27 small cubes that have no face painted, which means there are 125-27 = 98 cubes with at least one face painted.

98/125 = 78.4%
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