SOLUTION: A 3cm wooden cube is painted red on all surfaces. Imagine that it is cut into 1cm cubes. a) How many 1cm cubes have painted on 3 faces? b) How many 1cm cubes have painted on 2 fa

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Question 1107639: A 3cm wooden cube is painted red on all surfaces. Imagine that it is cut into 1cm cubes.
a) How many 1cm cubes have painted on 3 faces?
b) How many 1cm cubes have painted on 2 faces?
c) How many 1cm cubes have painted on 1 face?
d) How many 1cm cubes are not painted at all?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
There's no math to solve this.
You have to figure it out.
Answer by ikleyn(52767)   (Show Source): You can put this solution on YOUR website!
.
There is nothing easier to solve.


a)  How many 1cm cubes have painted on 3 faces?

    Those and only those that are located at the vertices (corners) of the 3x3x3 cube: exactly 8 small cubes.



b)  How many 1cm cubes have painted on 2 faces?

    Those and only those that are located at the edges but not attached to vertices: exactly one at each edge; 12 small cubes in all.



c)  How many 1cm cubes have painted on 1 face?

    Those and only those that are located at the center of each face and not attached NEITHER to vertices NOR edges: 
    exactly one at each face; 6 small cubes in all.



d)  How many 1cm cubes are not painted at all?

    Exactly 1 (one, ONE) located at the center of the 3x3x3 cube.

Check.   8 + 12 + 6 + 1 = 27 = 3*3*3.    ! Correct !



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