# Finding sides on giant wooden cube

• May 25th 2008, 01:49 PM
annie3993
Finding 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, 03:10 PM
TheEmptySet
Quote:

Originally Posted by annie3993
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!!

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.

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

I hope this helps.
• May 25th 2008, 03:22 PM
Soroban
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?

This is a 5 × 5 × 5 cube.

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 nine cubes in the center have one face painted green.
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: $12 \times 3 \:=\:\boxed{36}$ cubes with two green faces.

• May 25th 2008, 03:23 PM
galactus
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