Question 1099103: 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
Email. razamuh@hotmail.com
Answer by KMST(5328)   (Show Source):
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The big cube has 8 corners.
The  little cubes on those corners will have 3 faces painted.
The big cube has 12 edges.
There are 6 little cubes along each of those edges,
but the 2 at the ends are on a corner of the big cube.
We already figured out what happens with those little cubes.
The little cubes on the big cube's edges that are not on a corner
will have 2 faces painted.
There are 6-2=4 such little cubes on each of the 12 edges,
for a total of  little cubes with 2 faces painted.
There are also  little cubes forming the center of each big cube face
that will have only one face painted. You did not ask about those, but there are
 with exactly one face painted.
If you peel the outer layer of little cubes, you get a medium sized cube,
with 4 cm edges made up of  little cubes.
Those  little cubes have no face painted.
VERIFICATION:
aiming up the numbers of little cubes with exactly 0, 1, 2, and 3 faces painted we get
 and that makes sense,
because a big cube with 6 cm edges is made up of 
little cubes with 1 cm edges.
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