Sure, let's solve this step by step.

1. First, we need to understand that a cube has 6 faces. When a cube is painted on all faces, it means all the smaller cubes on the surface will have at least one face painted.

2. The cube is cut into 1331 smaller cubes. This means the original cube had a side of 11 units (since 11*11*11 = 1331).

3. The smaller cubes that are painted on only one face are those that lie in the center of each face of the original cube. These are not on the edge or the corner, so they are only painted on the side that was exposed.

4. Each face of the original cube is 11 units by 11 units, so it contains 121 smaller cubes. However, we must exclude the cubes along the edges to find the cubes painted on only one face. Each edge has 11 cubes, but the corner cubes are counted twice, so there are 11-2 = 9 cubes along each edge. There are 4 edges per face, so there are 4*9 = 36 cubes along the edges of each face.

5. Subtracting the edge cubes from the total number of cubes per face, we find there are 121 - 36 = 85 cubes painted on one face only per face of the original cube.

6. Since the original cube has 6 faces, the total number of smaller cubes painted on only one face is 6*85 = 510.

Question

Sure, let's solve this step by step.

1. First, we need to understand that a cube has 6 faces. When a cube is painted on all faces, it means all the smaller cubes on the surface will have at least one face painted.

2. The cube is cut into 1331 smaller cubes. This means the original cube had a side of 11 units (since 11*11*11 = 1331).

3. The smaller cubes that are painted on only one face are those that lie in the center of each face of the original cube. These are not on the edge or the corner, so they are only painted on the side that was exposed.

4. Each face of the original cube is 11 units by 11 units, so it contains 121 smaller cubes. However, we must exclude the cubes along the edges to find the cubes painted on only one face. Each edge has 11 cubes, but the corner cubes are counted twice, so there are 11-2 = 9 cubes along each edge. There are 4 edges per face, so there are 4*9 = 36 cubes along the edges of each face.

5. Subtracting the edge cubes from the total number of cubes per face, we find there are 121 - 36 = 85 cubes painted on one face only per face of the original cube.

6. Since the original cube has 6 faces, the total number of smaller cubes painted on only one face is 6*85 = 510.

Knowee AI · Accepted Answer

Sure, let's solve this step by step.

1. First, we need to understand that a cube has 6 faces. When a cube is painted on all faces, it means all the smaller cubes on the surface will have at least one face painted.

2. The cube is cut into 1331 smaller cubes. This means the original cube had a side of 11 units (since 11*11*11 = 1331).

3. The smaller cubes that are painted on only one face are those that lie in the center of each face of the original cube. These are not on the edge or the corner, so they are only painted on the side that was exposed.

4. Each face of the original cube is 11 units by 11 units, so it contains 121 smaller cubes. However, we must exclude the cubes along the edges to find the cubes painted on only one face. Each edge has 11 cubes, but the corner cubes are counted twice, so there are 11-2 = 9 cubes along each edge. There are 4 edges per face, so there are 4*9 = 36 cubes along the edges of each face.

5. Subtracting the edge cubes from the total number of cubes per face, we find there are 121 - 36 = 85 cubes painted on one face only per face of the original cube.

6. Since the original cube has 6 faces, the total number of smaller cubes painted on only one face is 6*85 = 510.

A cube painted blue on all faces is cut into 1331 cubes of equal size. How many cubes are painted on one face only?.726600486243

Question

A cube painted blue on all faces is cut into 1331 cubes of equal size. How many cubes are painted on one face only?

Solution

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