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A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?
- a)4
- b)6
- c)8
- d)10
Correct answer is option 'C'. Can you explain this answer?
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A solid cube is painted yellow, blue and black such that opposite face...
By the condition described in the question the cube can be divided as shown below. For the sake of simplicity, let the side of original cube be 12 units. So the new structure is as shown in image. Our desired cubes are marked with R. So a total of 4 and 4 = 8 cubes will have only one face painted.
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A solid cube is painted yellow, blue and black such that opposite face...
Given:
- A solid cube is painted yellow, blue, and black such that opposite faces are of the same color.
- The cube is cut into 36 cubes of two different sizes, 32 small and 4 big.
- None of the faces of the bigger cubes is painted blue.
To find: How many cubes have only one face painted?
Solution:
- Let's first draw the original cube and mark the opposite faces with the same color:
Y B Y
B B B
Y B Y
- The cube is cut into 36 cubes, 32 of which are small and 4 are big. We can assume that the big cubes are made up of 8 small cubes each, since each big cube has no blue faces and the only way to achieve this is by using 8 small cubes with no blue faces.
- Let's mark the big cubes in the original cube:
Y B Y
B 1 B
Y B Y
- We can see that there are 4 big cubes, marked as '1' in the above diagram.
- Now, let's count the number of cubes with only one face painted:
- The cubes with only one face painted are the cubes on the surface of the original cube that have only one painted face visible.
- There are 6 such cubes for each color (yellow and black), since there are 6 cubes on each face of the original cube and each face has only one color.
- Therefore, the total number of cubes with only one face painted is 6 + 6 + 6 = 18.
- Since each big cube is made up of 8 small cubes, we can count the number of small cubes that have no blue faces as follows:
- Each big cube has 6 faces visible on the surface of the original cube.
- Since none of these faces are blue, there are 3 colors left to paint the faces of each big cube.
- Therefore, each big cube has 3 faces painted with one color and 3 faces painted with the other color.
- This means that each big cube is made up of 4 small cubes of one color and 4 small cubes of the other color.
- Since there are 4 big cubes, there are a total of 16 small cubes with no blue faces.
- Therefore, the total number of cubes with only one face painted is 18, and the correct answer is option (C).
- A solid cube is painted yellow, blue, and black such that opposite faces are of the same color.
- The cube is cut into 36 cubes of two different sizes, 32 small and 4 big.
- None of the faces of the bigger cubes is painted blue.
To find: How many cubes have only one face painted?
Solution:
- Let's first draw the original cube and mark the opposite faces with the same color:
Y B Y
B B B
Y B Y
- The cube is cut into 36 cubes, 32 of which are small and 4 are big. We can assume that the big cubes are made up of 8 small cubes each, since each big cube has no blue faces and the only way to achieve this is by using 8 small cubes with no blue faces.
- Let's mark the big cubes in the original cube:
Y B Y
B 1 B
Y B Y
- We can see that there are 4 big cubes, marked as '1' in the above diagram.
- Now, let's count the number of cubes with only one face painted:
- The cubes with only one face painted are the cubes on the surface of the original cube that have only one painted face visible.
- There are 6 such cubes for each color (yellow and black), since there are 6 cubes on each face of the original cube and each face has only one color.
- Therefore, the total number of cubes with only one face painted is 6 + 6 + 6 = 18.
- Since each big cube is made up of 8 small cubes, we can count the number of small cubes that have no blue faces as follows:
- Each big cube has 6 faces visible on the surface of the original cube.
- Since none of these faces are blue, there are 3 colors left to paint the faces of each big cube.
- Therefore, each big cube has 3 faces painted with one color and 3 faces painted with the other color.
- This means that each big cube is made up of 4 small cubes of one color and 4 small cubes of the other color.
- Since there are 4 big cubes, there are a total of 16 small cubes with no blue faces.
- Therefore, the total number of cubes with only one face painted is 18, and the correct answer is option (C).
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A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer?
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A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer?.
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?a)4b)6c)8d)10Correct answer is option 'C'. Can you explain this answer?.
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