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Homework Help: Geometry 2

  1. Jun 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Ali is making solids out of cubes . Each cube has a volume of 27 cm^3. The diagram shows one solid Ali made . It has 10 faces and a volume of 108 cm^3. Ali made a solid out of the cubes that has 9 faces.What is the smallest volume in cm^3 the solid could have?

    2. Relevant equations

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Jun 15, 2010 #2
    Have you done any calculations yet? What's your attempt at this so far? :smile:
  4. Jun 16, 2010 #3
    I tried rearranging those cubes to get a solid with 9 faces. Any hints?
  5. Jun 16, 2010 #4
    Good start :smile: I've tried that approach too, but.. is it even possible?! :uhh:

    I can only seem to be able to get either 6, 8, or 10 sides, when arranging those 4 cubes, and I'm sure I've tried all possible combinations as I suppose you have done already as well.

    The question seemed to imply that only those 4 cubes were used, but not sure if maybe then you can use as many as you like. Would certainly seem to be more possible then.
  6. Jun 16, 2010 #5
    I think the question asks for as many cubes as you like.

    Start with
    1 cube: 5 faces;
    2 cubes: 5 faces, 10 faces;
    3 cubes: 5 faces, 8 faces, 10 faces, 15 faces;
    4 cubes: 5 faces, 8 faces, 10 faces, 13 faces, 15 faces, 20 faces;

    Now you try, and give me the answer.
    Last edited: Jun 16, 2010
  7. Jun 16, 2010 #6
    .. I see a pattern! :wink:
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