A cube 4 cm on each side is painted blue and cut into 64 one cm cubes. How many one-cm cubes are painted blue on exactly two faces?
Hmmm. I get 24, since there are 12 edges.
its 24 sure
To find out how many one-cm cubes are painted blue on exactly two faces, we need to visualize the cube and understand its structure.
First, let's consider the original cube that is 4 cm on each side. To calculate the number of one-cm cubes it contains, we need to determine the total number of cubes on all sides. Since each side has 4 cubes, we multiply that by 6 (which represents the six faces of a cube) to get a total of 24 cubes.
Now, let's think about how the original cube is cut into smaller one-cm cubes. Each edge of the original cube is divided into four smaller edges, and these smaller edges create four smaller cubes with each corner of the original cube. So, there are 4 x 4 x 4 = 64 smaller cubes.
Now, let's analyze the cubes that are painted blue on exactly two faces. To identify these cubes, we need to visualize how the edges and corners of the original cube are cut.
The cubes on the edges of the original cube have exactly two faces painted blue because they are exposed to the sides of the larger cube. There are 12 edge cubes in total (4 cubes per edge, and 12 edges in a cube).
Additionally, the cubes on the corners of the original cube have exactly two faces painted blue because they are exposed to two adjacent sides. There are 8 corner cubes in total.
Now, to calculate the total number of cubes painted blue on exactly two faces, we add the number of edge cubes and corner cubes together: 12 + 8 = 20.
Therefore, there are 20 one-cm cubes painted blue on exactly two faces in the larger cube.
The cubes with two sides painted must lie along the edges, except those at the corner, (they would have 3 sides painted
On each side I see 2 blocks that would be painted on 2 sides
so the number of blocks = 6x2 or 12