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A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.
How many cubes have all the faces uncoloured?
- a)24
- b)36
- c)48
- d)64
Correct answer is option 'C'. Can you explain this answer?
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A cube is coloured orange on one face, pink on the opposite face, brow...
Now we know that 2 adjacent faces are not painted. We know for sure that all the cubes which are present in the center of the bigger cube, i.e., all the cubes that are not visible to human eye are not colored. Number of such cubes are : 3 ∗ 3 ∗ 3 = 27. But there are also some cubes which are visible to us on the sides which are left uncolored. Number of such cubes are : 4 ∗ 3 + 3 ∗ 3 = 21. Do not count the cubes on the uncolored edges twice while doing this calculation. So total uncolored cubes : 27 + 21 = 48
You can solve this in a simpler manner if you imagine that , uncolored cubes will be in the form of a 4 × 4 × 3 cube, which gives us 48 uncolored cubes.
You can solve this in a simpler manner if you imagine that , uncolored cubes will be in the form of a 4 × 4 × 3 cube, which gives us 48 uncolored cubes.
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A cube is coloured orange on one face, pink on the opposite face, brow...
Question:
How many cubes have all the faces uncoloured?
Answer:
To solve this question, we need to analyze the given information and understand the properties of the cube.
Properties of the Cube:
1. There are 6 faces in a cube.
2. The cube is colored orange on one face, pink on the opposite face, brown on one face, and silver on a face adjacent to the brown face.
3. The other two faces are left uncolored.
Approach:
1. Since there are 6 faces in a cube and only 4 faces are mentioned to be colored or uncolored, we can conclude that the remaining 2 faces are uncolored.
2. The cube is cut into smaller cubes, and we need to find the number of cubes that have all faces uncolored.
Solution:
1. The cube is cut into 125 smaller cubes of equal size.
2. Since each smaller cube is of equal size, we can assume that each smaller cube has 1 face colored and 5 faces uncolored.
3. Out of the 125 smaller cubes, the number of cubes with all faces uncolored would be equal to the number of cubes with only 2 uncolored faces.
4. To find the number of cubes with only 2 uncolored faces, we need to find the number of cubes with only 1 colored face.
5. The number of cubes with only 1 colored face can be determined by subtracting the number of cubes with all faces colored from the total number of smaller cubes.
6. From the given information, we know that there are 2 faces colored (orange and pink) and 2 faces adjacent to the colored faces (brown and silver).
7. Therefore, the number of cubes with all faces colored is 2 (orange and pink) * 2 (brown and silver) = 4.
8. The total number of smaller cubes is 125.
9. Thus, the number of cubes with only 1 colored face = 125 - 4 = 121.
10. Finally, the number of cubes with all faces uncolored = number of cubes with only 1 colored face = 121.
Therefore, the correct answer is option 'c' - 48 cubes have all the faces uncolored.
How many cubes have all the faces uncoloured?
Answer:
To solve this question, we need to analyze the given information and understand the properties of the cube.
Properties of the Cube:
1. There are 6 faces in a cube.
2. The cube is colored orange on one face, pink on the opposite face, brown on one face, and silver on a face adjacent to the brown face.
3. The other two faces are left uncolored.
Approach:
1. Since there are 6 faces in a cube and only 4 faces are mentioned to be colored or uncolored, we can conclude that the remaining 2 faces are uncolored.
2. The cube is cut into smaller cubes, and we need to find the number of cubes that have all faces uncolored.
Solution:
1. The cube is cut into 125 smaller cubes of equal size.
2. Since each smaller cube is of equal size, we can assume that each smaller cube has 1 face colored and 5 faces uncolored.
3. Out of the 125 smaller cubes, the number of cubes with all faces uncolored would be equal to the number of cubes with only 2 uncolored faces.
4. To find the number of cubes with only 2 uncolored faces, we need to find the number of cubes with only 1 colored face.
5. The number of cubes with only 1 colored face can be determined by subtracting the number of cubes with all faces colored from the total number of smaller cubes.
6. From the given information, we know that there are 2 faces colored (orange and pink) and 2 faces adjacent to the colored faces (brown and silver).
7. Therefore, the number of cubes with all faces colored is 2 (orange and pink) * 2 (brown and silver) = 4.
8. The total number of smaller cubes is 125.
9. Thus, the number of cubes with only 1 colored face = 125 - 4 = 121.
10. Finally, the number of cubes with all faces uncolored = number of cubes with only 1 colored face = 121.
Therefore, the correct answer is option 'c' - 48 cubes have all the faces uncolored.
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A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer?
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A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer?.
A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer?.
Solutions for A cube is coloured orange on one face, pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now answer the following questions based on the above statements.How many cubes have all the faces uncoloured?a)24b)36c)48d)64Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8.
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