SOLUTION: Hi
a big solid cube is made of 27 small cubes of edge 2cm. If the outer of the big cube were painted, find the total area of the painted surfaces of the small cubes that had bee
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a big solid cube is made of 27 small cubes of edge 2cm. If the outer of the big cube were painted, find the total area of the painted surfaces of the small cubes that had bee
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Question 1124729: Hi
a big solid cube is made of 27 small cubes of edge 2cm. If the outer of the big cube were painted, find the total area of the painted surfaces of the small cubes that had been painted more than twice.
Thanks Found 2 solutions by ikleyn, jim_thompson5910:Answer by ikleyn(52781) (Show Source):
There are exactly 8 such small cubes - no one more and no one less.
These cubes are the corner cubes of the large cube.
Each of these cubes has exactly three painted faces.
So, the total area under the question is (2*2)*8*3 cm^2 = 96 cm^2.
You can put this solution on YOUR website! Since we're looking for cubes that have more than 2 painted faces, this means we're looking at the 8 corners (4 corners on top, 4 corners on the bottom)
I recommend looking at a 3x3 rubix cube for reference
The other cubes have been painted on exactly 2 faces (the edge cubes) or exactly 1 time (the middle-most cubes that are on the outside). The middle-most center cube isn't painted at all.
Each face that is painted is 2 by 2, so the area is 2*2 = 4 square cm. There are 3 of these painted faces for a given corner cube, so 3*4 = 12 square inches is the total so far. There are 8 of these corners giving 8*12 = 96.
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