is there a formula for working out how many cm cubes fit into say a 12*6*5 skeleton cuboid.
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 $\displaystyle 12 \times 6 \times 5$ cuboid, there will be: .$\displaystyle 12\cdot6\cdot5 \:=\:360$ unit cubes.
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 $\displaystyle L-2$ cubes.
There are 4 widths with $\displaystyle W - 2$ cubes.
There are 4 heights with $\displaystyle H-2$ cubes.
Total number of cubes: .$\displaystyle N \;=\;8 + 4(L-2) + 4(W-2) + 4(H-2)$
. . which simplifies to: .$\displaystyle N \;=\; 4(L+W+H-4)$
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