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If one face of a cube is painted red and then it is cut into 64 smaller cubes of equal size, how many smaller cubes will have exactly two faces painted?
- a)4
- b)8
- c)16
- d)24
Correct answer is option 'D'. Can you explain this answer?
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If one face of a cube is painted red and then it is cut into 64 smalle...
When a cube is cut into smaller cubes, the cubes at the edges (excluding the corners) will have exactly two faces painted.
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If one face of a cube is painted red and then it is cut into 64 smalle...
To solve this problem, we need to visualize the cube and understand how the smaller cubes are formed when it is cut.
Understanding the Cube:
A cube has 6 faces, and one of the faces is painted red. Let's consider this painted face as the bottom face of the cube. The other 5 faces are not painted.
Cutting the Cube:
When the cube is cut, it is divided into smaller cubes. Each cut is made parallel to the faces of the original cube. So, when we cut the cube, we can divide it into smaller cubes in a grid pattern.
Visualizing the Smaller Cubes:
Let's visualize the smaller cubes in a 4x4x4 grid. Each row on the grid represents a layer of smaller cubes.
Number of Smaller Cubes with 2 Painted Faces:
To determine the number of smaller cubes with exactly two faces painted, we need to analyze the cubes at the edges and corners of the grid.
Edge Cubes:
The cubes on the edges of the grid have three faces exposed. Therefore, none of these cubes will have exactly two faces painted.
Corner Cubes:
The cubes at the corners of the grid have three faces exposed as well. Hence, none of these cubes will have exactly two faces painted.
Interior Cubes:
The remaining cubes in the interior of the grid have only two faces exposed. These cubes will have exactly two faces painted.
Counting the Interior Cubes:
To count the number of interior cubes, we need to determine the number of cubes in the grid that are not on the edges or corners.
In each row, there are 4 cubes. Since there are 4 rows, there are a total of 4 x 4 = 16 cubes in the interior.
Therefore, the correct answer is option D) 24.
Understanding the Cube:
A cube has 6 faces, and one of the faces is painted red. Let's consider this painted face as the bottom face of the cube. The other 5 faces are not painted.
Cutting the Cube:
When the cube is cut, it is divided into smaller cubes. Each cut is made parallel to the faces of the original cube. So, when we cut the cube, we can divide it into smaller cubes in a grid pattern.
Visualizing the Smaller Cubes:
Let's visualize the smaller cubes in a 4x4x4 grid. Each row on the grid represents a layer of smaller cubes.
Number of Smaller Cubes with 2 Painted Faces:
To determine the number of smaller cubes with exactly two faces painted, we need to analyze the cubes at the edges and corners of the grid.
Edge Cubes:
The cubes on the edges of the grid have three faces exposed. Therefore, none of these cubes will have exactly two faces painted.
Corner Cubes:
The cubes at the corners of the grid have three faces exposed as well. Hence, none of these cubes will have exactly two faces painted.
Interior Cubes:
The remaining cubes in the interior of the grid have only two faces exposed. These cubes will have exactly two faces painted.
Counting the Interior Cubes:
To count the number of interior cubes, we need to determine the number of cubes in the grid that are not on the edges or corners.
In each row, there are 4 cubes. Since there are 4 rows, there are a total of 4 x 4 = 16 cubes in the interior.
Therefore, the correct answer is option D) 24.
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If one face of a cube is painted red and then it is cut into 64 smaller cubes of equal size, how many smaller cubes will have exactly two faces painted?a)4b)8c)16d)24Correct answer is option 'D'. Can you explain this answer?
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