there are 27 white cubes assembled to forma large cube.the outside surface of the large cube is painted red. the large cube is then separated into the 27 smaller cubes.how many of the small cubes will have red paint on exactly the following number of faces?
A= three faces
B= two faces
C= one face
D= no face
pick one ___________
visualize a 3x3x3 cube
D) the one cube in the middle will have no paint on it
C) the middle cube of each face, so 6 faces, so 6
B two faces,middle cubes joining two faces.
again , I can see 6 of those
A) wouldn't that be a corner cube?
How many of those are there?
so which one is the answer
A
B
C
d
There are 4 different question,
I answered 3 of those four you, and gave you the hint for A)
yeh so
A=1 cube
B=6 cubes
C=6 cubes
D=14 cubes
is this correct or not
wait i mean
A=14 cubes
b=6 cubes
c=6 cubes
d=1 cubes
A) How did you get 14???
look at a pair of playing dice, pick up one of them.
How many corners do you see?
Mine has 8
so its 8
yes
To determine how many small cubes will have red paint on a specific number of faces, we need to understand the arrangement of the 27 small cubes when formed into a large cube.
A large cube with 27 small cubes arranged into it will have a 3x3x3 structure. Each face of the large cube represents a layer of 9 small cubes.
Now let's analyze each option:
A) Three Faces: The only way for a small cube to have red paint on three faces is if it sits in one of the eight corners of the large cube. There are eight corners in a cube, so the answer is 8.
B) Two Faces: To calculate the number of small cubes with red paint on two faces, we need to consider two scenarios. First, we have the cubes located at the edges of the large cube, excluding the corners. There are 12 edges in a cube, and each edge contributes two small cubes with red paint on two faces, for a total of 24 cubes. The second scenario is the ones located in the middle of the faces of the large cube, excluding the corners and edges, which are 6. So, the answer is 24 + 6 = 30.
C) One Face: The small cubes located on the faces of the large cube, excluding the corners, edges, and center, have red paint on only one face. Each face has 1 cube in the center (1x1) and 4 cubes on the edges (2x2), resulting in 5 cubes per face. Since there are six faces in a cube, the total number of small cubes with red paint on one face is 6x5 = 30.
D) No Face: The remaining cubes that do not have red paint on any face are the ones located in the center of each face of the large cube, excluding the corners, edges, and the center cube. There are 9 cubes in total, one per face, and these will not have any red paint on their faces. Therefore, the answer is 9.
To summarize:
A) Three Faces: 8 small cubes
B) Two Faces: 30 small cubes
C) One Face: 30 small cubes
D) No Face: 9 small cubes
You can now choose the appropriate answer from the options provided.