A giant wooden cube is painted green on all 6 sides and then cut into 125identical, smaller cubes. How many of these smaller cubes are painted on exactly two faces?

i got 72, but I don't think its right...

THANX!!

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- May 25th 2008, 12:49 PMannie3993Finding sides on giant wooden cube
A giant wooden cube is painted green on all 6 sides and then cut into 125identical, smaller cubes. How many of these smaller cubes are painted on exactly two faces?

i got 72, but I don't think its right...

THANX!! - May 25th 2008, 02:10 PMTheEmptySet
Maybe this diagram will help.

P.S. Always try to draw a picture it really helps you see what is going on.

Attachment 6507

It looks like four groups of 3 on the top

four groups of 3 in the middle

and four groups of 3 on the bottom.

$\displaystyle 4(3)+4(3)+4(3)=4(9)=36$

I hope this helps. - May 25th 2008, 02:22 PMSoroban
Hello, annie3993!

Quote:

A giant wooden cube is painted green on all 6 sides and then cut into 125 identical smaller cubes.

How many of these smaller cubes are painted on exactly two faces?

A cube has 6 faces, 12 edges, and 8 corners (vertices).

Let's look at one face.Code:`* - * - * - * - * - *`

| 3 | 2 | 2 | 2 | 3 |

* - * - * - * - * - *

| 2 | 1 | 1 | 1 | 2 |

* - * - * - * - * - *

| 2 | 1 | 1 | 1 | 2 |

* - * - * - * - * - *

| 2 | 1 | 1 | 1 | 2 |

* - * - * - * - * - *

| 3 | 2 | 2 | 2 | 3 |

* - * - * - * - * - *

The four cubes in the corners have three faces painted green.

__On____each____edge__, there are*three*cubes with two green faces.

Since there are 12 edges, there are: $\displaystyle 12 \times 3 \:=\:\boxed{36}$ cubes with two green faces.

- May 25th 2008, 02:23 PMgalactus
See this thread. You may find it interesting.

http://www.mathhelpforum.com/math-he...-question.html

If yu go to the bottom you will see the general formula of 12(n-2). In your case, 12(5-2)=36