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Math Help - Finding sides on giant wooden cube

  1. #1
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    Red face Finding sides on giant wooden cube

    A giant wooden cube is painted green on all 6 sides and then cut into 125identical, smaller cubes. How many of these smaller cubes are painted on exactly two faces?


    i got 72, but I don't think its right...

    THANX!!
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  2. #2
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    Quote Originally Posted by annie3993 View Post
    A giant wooden cube is painted green on all 6 sides and then cut into 125identical, smaller cubes. How many of these smaller cubes are painted on exactly two faces?


    i got 72, but I don't think its right...

    THANX!!
    Maybe this diagram will help.

    P.S. Always try to draw a picture it really helps you see what is going on.

    Finding sides on giant wooden cube-capture.jpg

    It looks like four groups of 3 on the top

    four groups of 3 in the middle

    and four groups of 3 on the bottom.

    4(3)+4(3)+4(3)=4(9)=36

    I hope this helps.
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  3. #3
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    Hello, annie3993!

    A giant wooden cube is painted green on all 6 sides and then cut into 125 identical smaller cubes.
    How many of these smaller cubes are painted on exactly two faces?
    This is a 5 5 5 cube.

    A cube has 6 faces, 12 edges, and 8 corners (vertices).

    Let's look at one face.
    Code:
          * - * - * - * - * - *
          | 3 | 2 | 2 | 2 | 3 |
          * - * - * - * - * - *
          | 2 | 1 | 1 | 1 | 2 |
          * - * - * - * - * - *
          | 2 | 1 | 1 | 1 | 2 |
          * - * - * - * - * - *
          | 2 | 1 | 1 | 1 | 2 |
          * - * - * - * - * - *
          | 3 | 2 | 2 | 2 | 3 |
          * - * - * - * - * - *
    The nine cubes in the center have one face painted green.
    The four cubes in the corners have three faces painted green.

    On each edge, there are three cubes with two green faces.

    Since there are 12 edges, there are: 12 \times 3 \:=\:\boxed{36} cubes with two green faces.

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  4. #4
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    See this thread. You may find it interesting.

    http://www.mathhelpforum.com/math-he...-question.html

    If yu go to the bottom you will see the general formula of 12(n-2). In your case, 12(5-2)=36
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