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 1119044: 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?------
I need explanation
Reguards Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! There are 1cm cubes in all.
A. Those with (exactly) 2 faces painted red will be the cubes that share an edge (but not corners):
How many of them are there? There are 4 edges (each with 4 small cubes) on the front face, 4 on the back, and 4 edges that connect front to back. That 4x(4+4+4) = small cubes.
B. The corners of the large cube are the only places where 3 small cube faces come together to be painted red. There are 8 corners, so small cubes will have 3 faces painted red.
C. Those with no faces painted red will be the "interior large cube" which is comprised of 4x4x4 small cubes (we peel away one layer of small cubes all the way around the large cube): 4x4x4 = small cubes will not be painted red.
[ As a check: The difference between 216 and the sum of A,B,C (120) is the number of small cubes with exactly 1 face painted red, and those are 6 faces x 4x4 cubes per face or 6x16 = 96 (and 216-120 = 96) ].
