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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?
Iluv: that's the number of ubit cubes, but there are cubes with side length 2, side length 3, and so on...
6 Answers
- NotEasilyFooledLv 51 decade agoFavorite 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 51 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
^_^
- 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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