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A cube painted blue on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?
- a)6
- b)4
- c)8
- d)12
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A cube painted blue on all faces is cut into 27 small cubes of equal s...
Understanding the Cube Cutting Process
When a large cube is cut into smaller cubes, it helps to visualize how the smaller cubes relate to the painted surfaces of the original cube.
Cube Dimensions
- The original cube is a 3x3x3 configuration, resulting in 27 smaller cubes (3 cubes along each edge).
Identifying Painted Faces
- Each face of the original cube is painted blue. When we cut it into smaller cubes, we need to consider how many of these smaller cubes have only one face painted.
Location of Small Cubes
- Corner Cubes: There are 8 corner cubes. Each of these has 3 faces painted.
- Edge Cubes: There are 12 edge cubes. Each of these has 2 faces painted.
- Face Cubes: The cubes located in the center of each face (not touching the edges) are the ones with only 1 face painted.
Counting Cubes with One Face Painted
- Each of the 6 faces of the cube has 1 center cube that is painted on only one face.
- Therefore, there are 6 face cubes in total, but only 1 from each face, leading us to identify that there are specifically 6 cubes that have only one face painted.
Final Tally
- After analyzing the configuration, we conclude that there are indeed 6 small cubes that are painted on only one face, confirming that the correct answer is option 'A'.
When a large cube is cut into smaller cubes, it helps to visualize how the smaller cubes relate to the painted surfaces of the original cube.
Cube Dimensions
- The original cube is a 3x3x3 configuration, resulting in 27 smaller cubes (3 cubes along each edge).
Identifying Painted Faces
- Each face of the original cube is painted blue. When we cut it into smaller cubes, we need to consider how many of these smaller cubes have only one face painted.
Location of Small Cubes
- Corner Cubes: There are 8 corner cubes. Each of these has 3 faces painted.
- Edge Cubes: There are 12 edge cubes. Each of these has 2 faces painted.
- Face Cubes: The cubes located in the center of each face (not touching the edges) are the ones with only 1 face painted.
Counting Cubes with One Face Painted
- Each of the 6 faces of the cube has 1 center cube that is painted on only one face.
- Therefore, there are 6 face cubes in total, but only 1 from each face, leading us to identify that there are specifically 6 cubes that have only one face painted.
Final Tally
- After analyzing the configuration, we conclude that there are indeed 6 small cubes that are painted on only one face, confirming that the correct answer is option 'A'.
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Community Answer
A cube painted blue on all faces is cut into 27 small cubes of equal s...
The cubes having only one face painted are the cubes which lie at the centre of each face of big cube. There are 6 faces of a cube. So, required no. of cubes having one face painted = 6
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A cube painted blue on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?a)6b)4c)8d)12Correct answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A cube painted blue on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?a)6b)4c)8d)12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube painted blue on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on one face only?a)6b)4c)8d)12Correct answer is option 'A'. Can you explain this answer?.
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