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Directions: A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.
How many smaller cubes have no face coloured?
How many smaller cubes have no face coloured?
- a)24
- b)16
- c)8
- d)10
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Directions: A cube is coloured red on all of its faces. It is then cut...
Understanding the Cube
A cube is a three-dimensional shape with six equal square faces. When we paint it red on all sides and then cut it into smaller cubes, we need to analyze how many of these smaller cubes will have no red paint on any face.
Cutting the Cube
The given cube is cut into 64 smaller cubes. This means the cube is divided into a 4x4x4 grid (since 4 * 4 * 4 = 64). Each smaller cube will have a side length that is one-fourth of the original cube's side length.
Identifying Inner Cubes
To find the cubes with no red paint, we need to consider only the inner cubes. The outer layer of cubes will have at least one face painted red.
- The outer layer consists of the cubes on the edges and corners of the original cube.
- Only the cubes that are completely surrounded by other cubes will be unpainted.
Counting the Inner Cubes
In a 4x4x4 cube, the inner cubes are located in the center, away from any outer face.
- Dimensions of the Inner Cube:
The inner cube formed by removing the outer layer has dimensions 2x2x2 (since we remove one layer from each side).
- Calculating Inner Cubes:
The total number of smaller cubes in this inner 2x2x2 cube is 2 * 2 * 2 = 8.
Conclusion
Thus, the total number of smaller cubes that have no face coloured is 8.
The correct answer is option 'C'.
A cube is a three-dimensional shape with six equal square faces. When we paint it red on all sides and then cut it into smaller cubes, we need to analyze how many of these smaller cubes will have no red paint on any face.
Cutting the Cube
The given cube is cut into 64 smaller cubes. This means the cube is divided into a 4x4x4 grid (since 4 * 4 * 4 = 64). Each smaller cube will have a side length that is one-fourth of the original cube's side length.
Identifying Inner Cubes
To find the cubes with no red paint, we need to consider only the inner cubes. The outer layer of cubes will have at least one face painted red.
- The outer layer consists of the cubes on the edges and corners of the original cube.
- Only the cubes that are completely surrounded by other cubes will be unpainted.
Counting the Inner Cubes
In a 4x4x4 cube, the inner cubes are located in the center, away from any outer face.
- Dimensions of the Inner Cube:
The inner cube formed by removing the outer layer has dimensions 2x2x2 (since we remove one layer from each side).
- Calculating Inner Cubes:
The total number of smaller cubes in this inner 2x2x2 cube is 2 * 2 * 2 = 8.
Conclusion
Thus, the total number of smaller cubes that have no face coloured is 8.
The correct answer is option 'C'.
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Directions: A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.How many smaller cubes have no face coloured?a)24b)16c)8d)10Correct answer is option 'C'. Can you explain this answer? for Class 6 2026 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Directions: A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.How many smaller cubes have no face coloured?a)24b)16c)8d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 6 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. The smaller cubes so obtained are now separated.How many smaller cubes have no face coloured?a)24b)16c)8d)10Correct answer is option 'C'. Can you explain this answer?.
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