is there a formula for working out how many cm cubes fit into say a 12*6*5 skeleton cuboid.

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- Jan 6th 2011, 04:23 AMpeter2727skeleton cuboid
is there a formula for working out how many cm cubes fit into say a 12*6*5 skeleton cuboid.

- Jan 6th 2011, 04:42 AMSoroban
Hello, peter2727!

Quote:

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(1 x 1 x 1),*unit cubes*

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

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

- Jan 6th 2011, 04:47 AMProve It
How many cubes fit in a row?

How many rows?

How many layers? - Jan 6th 2011, 05:14 AMpeter2727
no sorry i meant to say a skeleton cuboid not a solid

- Jan 6th 2011, 07:21 AMSoroban
He4llo, peter2727!

Quote:

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 theof the cuboid,*outline*

. . 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: .$\displaystyle N \;=\; 4(L+W+H-4)$

- Jan 6th 2011, 07:27 AMalexmahone
- Jan 6th 2011, 08:07 AMpeter2727
Soroban

thanks for that however someone else said it was 4(l+w+h) -16 can that be the case - Jan 6th 2011, 08:10 AMpeter2727
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