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Math Help - skeleton cuboid

  1. #1
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    skeleton cuboid

    is there a formula for working out how many cm cubes fit into say a 12*6*5 skeleton cuboid.
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  2. #2
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    Hello, peter2727!

    Is there a formula for working out how many cm cubes
    fit into, say, a 12 x 6 x 5 cuboid?

    If your "cm cubes" are unit cubes (1 x 1 x 1),

    . . the number of cubes is simply the product of those dimensions.


    For a 12 \times 6 \times 5 cuboid, there will be: . 12\cdot6\cdot5 \:=\:360 unit cubes.

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  3. #3
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    How many cubes fit in a row?
    How many rows?
    How many layers?
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  4. #4
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    no sorry i meant to say a skeleton cuboid not a solid
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  5. #5
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    He4llo, peter2727!

    i meant to say a skeleton cuboid, not a solid.

    I saw the word "skeleton", but didn't know what it meant.
    . . (And I'm still not sure.)

    If you mean that the unit cubes form the outline of the cuboid,
    . . we can invent a formula.


    There are 8 cubes at the vertices (one in each "corner").

    There are 4 lengths with L-2 cubes.
    There are 4 widths with W - 2 cubes.
    There are 4 heights with H-2 cubes.

    Total number of cubes: . N \;=\;8 + 4(L-2) + 4(W-2) + 4(H-2)

    . . which simplifies to: . N \;=\; 4(L+W+H-4)

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  6. #6
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    Quote Originally Posted by Soroban View Post
    He4llo, peter2727!


    I saw the word "skeleton", but didn't know what it meant.
    . . (And I'm still not sure.)

    If you mean that the unit cubes form the outline of the cuboid,
    . . we can invent a formula.


    There are 8 cubes at the vertices (one in each "corner").

    There are 4 lengths with L-2 cubes.
    There are 4 widths with W - 2 cubes.
    There are 4 heights with H-2 cubes.

    Total number of cubes: . N \;=\;8 + 4(L-2) + 4(W-2) + 4(H-2)

    . . which simplifies to: . N \;=\; 4(L+W+H-4)

    That's not what he meant. He just means that the cuboid is hollow, not solid.

    Edit: I stand corrected.
    Last edited by alexmahone; January 6th 2011 at 09:59 AM. Reason: Post #7, 8 show that I was mistaken.
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  7. #7
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    Soroban
    thanks for that however someone else said it was 4(l+w+h) -16 can that be the case
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  8. #8
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    8 corners
    4 square rods of length (L – 2)
    4 square rods of length (B – 2)
    4 square rods of length (H – 2)
    Let C = number of cubes in the model.
    Then C = 8 + 4(L – 2) + 4(B – 2) + 4(H – 2)
    C = 4(L + B + H) – 16 or C = 4(L + B + H – 4)
    C = 4(12 + 6 + 10) – 16
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