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A cube is 6 cm in length, breadth and height. It is painted red on two opposite faces, black on the other two opposite faces and green on the left over faces. It is then cut into 216 cubes of side 1 cm. How many small cubes have no face painted?
- a)16
- b)8
- c)64
- d)24
Correct answer is option 'C'. Can you explain this answer?
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A cube is 6 cm in length, breadth and height. It is painted red on two...
From the given question
Number of small cubes have no face painted
= (6 – 2)3 = (4)3 = 64
So the number of small cubes have no face painted is 64.
Number of small cubes have no face painted
= (6 – 2)3 = (4)3 = 64
So the number of small cubes have no face painted is 64.
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A cube is 6 cm in length, breadth and height. It is painted red on two...
Given:
- A cube with dimensions 6 cm x 6 cm x 6 cm
- Two opposite faces are painted red
- Two opposite faces are painted black
- The remaining faces are painted green
- The cube is then cut into 216 smaller cubes of 1 cm x 1 cm x 1 cm
To determine the number of small cubes that have no face painted, we need to analyze the structure of the larger cube and identify the cubes that are completely surrounded by other cubes.
Identifying the Inner Cubes:
1. The larger cube has dimensions of 6 cm x 6 cm x 6 cm.
2. The outermost layer of the larger cube consists of small cubes that have at least one face painted.
3. The inner layer of the larger cube consists of small cubes that are surrounded by other cubes on all sides and therefore have no face painted.
4. The inner layer can be visualized as a smaller cube with dimensions 4 cm x 4 cm x 4 cm, which is obtained by subtracting 1 cm from each side of the larger cube.
Calculating the Number of Inner Cubes:
1. The number of small cubes in the inner layer can be calculated by multiplying the number of cubes in each dimension.
- Number of cubes in each dimension = (Side length of the inner layer)^3
- Number of cubes in each dimension = 4^3 = 64 cubes
2. Therefore, the total number of small cubes that have no face painted is 64.
Hence, the correct answer is option 'C' - 64 cubes.
- A cube with dimensions 6 cm x 6 cm x 6 cm
- Two opposite faces are painted red
- Two opposite faces are painted black
- The remaining faces are painted green
- The cube is then cut into 216 smaller cubes of 1 cm x 1 cm x 1 cm
To determine the number of small cubes that have no face painted, we need to analyze the structure of the larger cube and identify the cubes that are completely surrounded by other cubes.
Identifying the Inner Cubes:
1. The larger cube has dimensions of 6 cm x 6 cm x 6 cm.
2. The outermost layer of the larger cube consists of small cubes that have at least one face painted.
3. The inner layer of the larger cube consists of small cubes that are surrounded by other cubes on all sides and therefore have no face painted.
4. The inner layer can be visualized as a smaller cube with dimensions 4 cm x 4 cm x 4 cm, which is obtained by subtracting 1 cm from each side of the larger cube.
Calculating the Number of Inner Cubes:
1. The number of small cubes in the inner layer can be calculated by multiplying the number of cubes in each dimension.
- Number of cubes in each dimension = (Side length of the inner layer)^3
- Number of cubes in each dimension = 4^3 = 64 cubes
2. Therefore, the total number of small cubes that have no face painted is 64.
Hence, the correct answer is option 'C' - 64 cubes.
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