a cube is painted blue,then cut into 27 smaller cubes.how many of the smaller cubes have only two side painted/ggggggggggg
the cut cube must be 3 by 3 by 3
the only cubes that are painted on 2 sides would be the middle cubes along each edge.
There would be 12 of those.
(make a sketch to see the different cases)
none visible : 1
one visible : 6
two visible : 12
three visible : 8
total = 27
To find out how many of the smaller cubes have only two sides painted, we need to understand the pattern in which the larger cube was cut.
A standard way to cut a larger cube into smaller cubes is to divide each side of the larger cube into equal sections. In this case, since there are 27 smaller cubes, we can assume that the larger cube was cut into 3x3x3 smaller cubes.
To visualize this, imagine a 3x3x3 grid of smaller cubes, where each row, column, and layer consists of 3 smaller cubes.
When a cube is cut into smaller cubes, all of the smaller cubes on the outer layer will have two sides painted since they are exposed to the initial painting.
The outer layer consists of smaller cubes on the front face, back face, left face, right face, top face, and bottom face. There are 4 smaller cubes on each face (except for the center one), so each face consists of 4 smaller cubes, and there are 6 faces in total. This results in a total of 4x6 = 24 smaller cubes on the outer layer with exactly two sides painted.
Hence, out of the 27 smaller cubes, 24 of them have exactly two sides painted.
If a cube is painted blue and then cut into 27 smaller cubes, we can determine how many of the smaller cubes have only two sides painted by visualizing the cube.
A cube has 6 faces in total. When the cube is cut, each face can be covered by either another cube or exposed.
Since the cube is cut into 27 smaller cubes, we can calculate how many smaller cubes have two sides painted by examining the outer layer.
Each face of the outer layer consists of four smaller cubes. Since there are six faces, there will be a total of 6 x 4 = 24 smaller cubes in the outer layer.
Therefore, out of the 27 smaller cubes, 24 cubes will have two sides painted.