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A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size?
Most Upvoted Answer
A cube is painted red on two adjacent surface and black on the surface...
Solution:
Given:
A cube painted red on two adjacent surfaces, black on the surfaces opposite to red surfaces, and green on the remaining faces.
To find:
The number of smaller cubes of equal size when the given cube is cut.
Solution:
When a cube is cut into smaller cubes of equal size, the number of smaller cubes can be found by counting the number of cubes in each row, column, and layer.
Number of cubes in each row:
There are 4 rows in each direction (x, y, z), and each row contains 4 cubes.
Therefore, the total number of cubes in each row is 4 x 4 = 16.
Number of cubes in each column:
There are 4 columns in each direction (x, y, z), and each column contains 4 cubes.
Therefore, the total number of cubes in each column is 4 x 4 = 16.
Number of cubes in each layer:
There are 4 layers in each direction (x, y, z), and each layer contains 16 cubes.
Therefore, the total number of cubes in each layer is 16 x 4 = 64.
Total number of cubes:
The total number of cubes can be found by multiplying the number of cubes in each row, column, and layer.
Therefore, the total number of cubes is 16 x 16 x 64 = 16,384.
Hence, the given cube can be cut into 16,384 smaller cubes of equal size.
Given:
A cube painted red on two adjacent surfaces, black on the surfaces opposite to red surfaces, and green on the remaining faces.
To find:
The number of smaller cubes of equal size when the given cube is cut.
Solution:
When a cube is cut into smaller cubes of equal size, the number of smaller cubes can be found by counting the number of cubes in each row, column, and layer.
Number of cubes in each row:
There are 4 rows in each direction (x, y, z), and each row contains 4 cubes.
Therefore, the total number of cubes in each row is 4 x 4 = 16.
Number of cubes in each column:
There are 4 columns in each direction (x, y, z), and each column contains 4 cubes.
Therefore, the total number of cubes in each column is 4 x 4 = 16.
Number of cubes in each layer:
There are 4 layers in each direction (x, y, z), and each layer contains 16 cubes.
Therefore, the total number of cubes in each layer is 16 x 4 = 64.
Total number of cubes:
The total number of cubes can be found by multiplying the number of cubes in each row, column, and layer.
Therefore, the total number of cubes is 16 x 16 x 64 = 16,384.
Hence, the given cube can be cut into 16,384 smaller cubes of equal size.
Community Answer
A cube is painted red on two adjacent surface and black on the surface...
The larger cube is cut into 64 smaller cubes. This implies that the edge of a smaller cube is one-fourth that of the larger cube. We know that the two adjacent faces are painted red and the two faces opposite to these faces are painted black. This implies that the top and the bottom faces are painted green. Thus, there are two edges where the faces painted red and black meet, and each edge has four cubes. Thus, there are totally 88 smaller cubes on each face. So, there are 32 smaller cubes which have at least one of their faces green. The remaining 64 - 32 = 32 smaller cubes have none of their faces green.
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A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size?
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A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size?.
A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube is painted red on two adjacent surface and black on the surfaces opposite to red surfaces and green on the remaining faces now the cube is cut into sixty four smaller cubes of equal size?.
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