SOLUTION: Please solve this question, A cube with sides of 6cm is built out of 1 cm cubes. The outside of the large cube is painted red. How many of the smaller 1cm cubes will have: A.

Question 1098956: Please solve this question,
A cube with sides of 6cm is built out of 1 cm cubes.
The outside of the large cube is painted red.
How many of the smaller 1cm cubes will have:
A. 2 faces painted red? -------
B. 3 faces painted red? -------
C. No red faces?------
Reguards
Raza
razamuh@hotmail.com
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Why don't you do some thinking on your own to solve this problem? You won't learn anything if we simply give you the answer.

There are four different places a small cube can be on the large cube to have different numbers of faces painted:
(1) corners -- 3 faces get painted
(2) edges (but not corners) -- 2 faces get painted
(3) on a face of the large cube (but not an edge or a corner) -- 1 face painted
(4) the interior of the cube -- 0 faces painted

Draw a picture, or try to visualize, how many of the small cubes in the 6x6x6 large cube are in each of those four positions.

Note that if you find all four of the answers, the total should be 6*6*6 = 216, so you will be able to check to see if the numbers you got are correct.

You say you still couldn't get the answer....
Okay, I'll help you along.

(1) The small cubes in the corners each have 3 faces painted. How many corners does a 6x6x6 cube (or ANY cube) have?

(2) The small cubes along the edges, except for the ones in the corners, each have 2 faces painted. How many edges does any cube have? How many small cubes are there on each edge of a 6x6x6 cube, not counting the corner cubes?

(3) It's not part of the problem as you show it, but the small cubes with one face painted are the ones on a face of the large cube that are not on an edge or in a corner. There are 6 faces on the cube; on each of those faces of a 6x6x6 cube, how many small cubes are there that are not on an edge or in a corner? Multiply that number by 6 to find the total number of small cubes with one face painted.

(4) The small cubes with no faces painted are the ones that are not anywhere on the surface of the 6x6x6 cube. If you think of stripping the outer layer off of a 6x6x6 cube, what you are left with is a 4x4x4 cube. The number of small cubes in that 4x4x4 cube is the number that have no faces painted.
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