1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook