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A Cube is segmented into 1728 equal tiny cubes and having corner named as U, V, W, X, Y, Z, A and B. Before dividing the cube, each face of it is varnished with different colours. How many tiny cubes will be formed having more than one colour?
- a)55
- b)120
- c)112
- d)128
Correct answer is option 'D'. Can you explain this answer?
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A Cube is segmented into 1728 equal tiny cubes and having corner named...
Problem Analysis:
We are given a cube that is segmented into 1728 equal tiny cubes. Each face of the cube is varnished with different colors. We need to determine the number of tiny cubes that will have more than one color.
Solution:
To solve this problem, we will break it down into smaller steps:
Step 1: Determine the number of cubes with no painted faces.
- Each face of the cube has been painted, so there are no cubes with no painted faces.
Step 2: Determine the number of cubes with one painted face.
- Each face of the cube has been painted, so there are no cubes with only one painted face.
Step 3: Determine the number of cubes with two painted faces.
- Each edge of the cube has two cubes, and there are 12 edges in total.
- Therefore, there are 12 * 2 = 24 cubes with two painted faces.
Step 4: Determine the number of cubes with three painted faces.
- Each corner of the cube has three cubes, and there are 8 corners in total.
- Therefore, there are 8 * 3 = 24 cubes with three painted faces.
Step 5: Determine the number of cubes with four painted faces.
- Each face of the cube has four cubes, and there are 6 faces in total.
- Therefore, there are 6 * 4 = 24 cubes with four painted faces.
Total:
The total number of cubes with more than one color is the sum of the cubes with two, three, and four painted faces:
24 + 24 + 24 = 72
Conclusion:
Therefore, there are 72 tiny cubes that will have more than one color.
We are given a cube that is segmented into 1728 equal tiny cubes. Each face of the cube is varnished with different colors. We need to determine the number of tiny cubes that will have more than one color.
Solution:
To solve this problem, we will break it down into smaller steps:
Step 1: Determine the number of cubes with no painted faces.
- Each face of the cube has been painted, so there are no cubes with no painted faces.
Step 2: Determine the number of cubes with one painted face.
- Each face of the cube has been painted, so there are no cubes with only one painted face.
Step 3: Determine the number of cubes with two painted faces.
- Each edge of the cube has two cubes, and there are 12 edges in total.
- Therefore, there are 12 * 2 = 24 cubes with two painted faces.
Step 4: Determine the number of cubes with three painted faces.
- Each corner of the cube has three cubes, and there are 8 corners in total.
- Therefore, there are 8 * 3 = 24 cubes with three painted faces.
Step 5: Determine the number of cubes with four painted faces.
- Each face of the cube has four cubes, and there are 6 faces in total.
- Therefore, there are 6 * 4 = 24 cubes with four painted faces.
Total:
The total number of cubes with more than one color is the sum of the cubes with two, three, and four painted faces:
24 + 24 + 24 = 72
Conclusion:
Therefore, there are 72 tiny cubes that will have more than one color.
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Community Answer
A Cube is segmented into 1728 equal tiny cubes and having corner named...
x = Cube root of 1728 = 12. More than one colour means two or more colours. So total number of cubes whose two faces are varnished = (x - 2) × number of edges = (12 - 2) × 12 = 120. The three varnished cubes have the number of corners = 8. So total number of required cubes = 120 + 8 = 128.
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A Cube is segmented into 1728 equal tiny cubes and having corner named as U, V, W, X, Y, Z, A and B. Before dividing the cube, each face of it is varnished with different colours. How many tiny cubes will be formed having more than one colour?a)55b)120c)112d)128Correct answer is option 'D'. Can you explain this answer?
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