<p>A large solid cube is assembled by gluing together
identical unpainted small cubic blocks. All six faces
of the large cube are then painted red. If exactly 27 of
the small cubic blocks that make up the large cube have
no red paint on them, how many small cubic blocks
make up the large cube?</p>
<p>Completly stumped, any help?</p>
<p>I didnt really read the ?, but if it's what I think it is, you'd answer it like this:
All of the outer faces are painted red. So to find the number not painted, imagine a smaller cube inside teh larger one with no external sides. There will be a total of (n-2)^3 cubes here. so we have the equation, (n-2)^3=27
n=5. That means there are 5 cubes per side, so there are a total of 5^3 or 125 cubes in the larger cube.</p>
<p>There is 1 block in the center. To cover that block on all sides, the larger cube would have to be made up of 27 blocks (length and width of 3). To cover the 27 blocks on all sides (adding the red ones), the new cube would have to have 125 blocks (length and width of 5). So the number of blocks total is simply 125.</p>
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