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 ___________
To find out how many small cubes will have red paint on exactly a certain number of faces, we can break down the question into parts.
1. A = Three faces:
A cube has 6 faces in total. Since all the outside surfaces of the large cube are painted red, a small cube can have a maximum of 3 faces painted red. Therefore, to have exactly 3 faces red, a small cube must have all its outer faces painted. Since we have 27 small cubes, each with 6 faces, the number of small cubes with exactly 3 faces painted red is 27.
2. B = Two faces:
To have exactly 2 faces painted red, a small cube must have two opposite faces painted. There are 12 small cubes that form the edges of the large cube, and each of them will have exactly 2 faces painted red. So, the number of small cubes with exactly 2 faces painted red is 12.
3. C = One face:
To have exactly 1 face painted red, a small cube must have a corner face painted. There are 8 small cubes forming the corners of the large cube, and each of them will have exactly 1 face painted red. So, the number of small cubes with exactly 1 face painted red is 8.
4. D = No faces:
To have no faces painted red, a small cube must have all its faces on the inside of the large cube. Since the large cube is separated into 27 small cubes, all of them will have their faces on the inside. Therefore, the number of small cubes with no faces painted red is 27.
In summary, the answer is:
A = 27 cubes
B = 12 cubes
C = 8 cubes
D = 27 cubes
You can select one of the options based on the number of small cubes with the respective amount of red-painted faces.