Question 58209: A 12 centimeter cube (i.e. 12x12x12) was painted red on the outside. The cube was then cut into one centimeter cubes. How many of these smaller cubes have paint on one side? Two sides? Three sides? No sides? (hint: examine smaller cubes first) show/explain the procedure used.
Answer by rcmcc(152)   (Show Source):
You can put this solution on YOUR website! I believe this is a higher thinking question, where you have to do a step removal process.
knowing a cube each side has 12 rows of 12 squares, when you subtract the outside squares (they have paint on 2 and 3 sides, you get 10 rows of 10 squares
by 6 sides there are 600 squares with one side painted
each corner of the square would have 3 sides painted, as there are 8 corners, 8 cubes have 3 sides painted.
now all we have left are the outside painted cubes, because the corners are missing, there is 10 per row, (12 per row subtracting 2 corners in a row=10 per row)
there are 12 rows on a cube, (4 on the top, 4 on the bottom, and 4 on the sides, because they all share sides we can not state 4X6 sides we have to logically subtract the sides.
because there are 12 rows with 10 in a row, there is 120 cubes with 2 sides painted.
last, there are 10 rows, 10 columns, and 10 stacks left, hence there is 1000 unpainted cubes. here is the completed list.
8=cubes with 3 painted sides
120=cubes with 2 painted sides
600=cubes with 1 painted side
1000=cubes with no painted sides.
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1728 cubes in total
check, 12x12x12=1728, so we have accounted for all the squares.
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