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Jimbo
Lv 5
Jimbo asked in Science & MathematicsMathematics · 1 decade ago

A problem of cubes?

A rectangular structure is composed of unit cubes. Its dimensions are 11 by 17 by 23. How many cubes are contained within the structure?

Update:

Iluv: that's the number of ubit cubes, but there are cubes with side length 2, side length 3, and so on...

6 Answers

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  • 1 decade ago
    Favorite Answer

    If the cubes are allowed to overlap, I think we have

    11 x 17 x 23 = 4301 cubes of size 1

    10 x 16 x 22 = 3520 cubes of size 2

    9 x 15 x 21 = 2835 cubes of size 3

    8 x 14 x 20 = 2240 cubes of size 4

    7 x 13 x 19 = 1729 cubes of size 5

    6 x 12 x 18 = 1296 cubes of size 6

    5 x 11 x 17 = 935 cubes of size 7

    4 x 10 x 16 = 640 cubes of size 8

    3 x 9 x 15 = 405 cubes of size 9

    2 x 8 x 14 = 224 cubes of size 10

    1 x 7 x 13 = 91 cubes of size 11

    So the total number of cubes is 18216

  • kevin!
    Lv 5
    1 decade ago

    The number of n x n x n cubes in an a x b x c rectangular structure (where a, b, c, and n are integers) is (a - n + 1)(b - n + 1)(c - n + 1)

    Therefore, the number of cubes contained is:

    11 x 17 x 23 + 10 x 16 x 22 + 9 x 15 x 21 + 8 x 14 x 20 + 7 x 13 x 19 + 6 x 12 x 18 + 5 x 11 x 17 + 4 x 10 x 16 + 3 x 9 x 15 + 2 x 8 x 14 + 1 x 7 x 13 + 0 x 6 x 12

    = 18216 cubes

    ^_^

  • number of cubes in the structure are 11*17*23 = 4301

  • 1 decade ago

    First of all you get volume

    Volume V of cuboid (rectangle structure) = L*B*H

    V = 11*17*23

    V = 4301 unit cube

    thus 4301 cubes is the answer

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  • 1 decade ago

    infinite

  • 1 decade ago

    ur bra is coming out

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