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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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?
- a)2
- b)4
- c)8
- d)6
Correct answer is option 'C'. Can you explain this answer?
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A Cube is segmented into 1728 equal tiny cubes and having corner named...
Problem Analysis:
- The cube is divided into 1728 equal tiny cubes, which means it is a 12x12x12 cube.
- Each face of the cube is varnished with different colors, with two portions having the same color and two portions having different colors.
- We need to determine the number of tiny cubes that will have all three colors.
Solution:
To solve this problem, we need to analyze the different segments of the cube and determine the number of tiny cubes that will have all three colors.
1. Corners:
There are eight corners in the cube: U, V, W, X, Y, Z, A, and B.
- Each corner is formed by the intersection of three faces.
- Since each face has two segments with the same color and two segments with different colors, each corner will have all three colors.
- Therefore, there are 8 corners in total that have all three colors.
2. Edges:
There are 12 edges in the cube.
- Each edge is formed by the intersection of two faces.
- Since each face has two segments with the same color and two segments with different colors, each edge will have two segments with the same color and one segment with a different color.
- Therefore, none of the edges will have all three colors.
3. Faces:
There are 6 faces in the cube.
- Each face is formed by dividing the cube into a 12x12 grid.
- Each face has two segments with the same color and two segments with different colors.
- Each face will have 6 segments with the same color and 6 segments with a different color.
- Therefore, none of the faces will have all three colors.
4. Inner Cubes:
There are (12-2) x (12-2) x (12-2) = 10x10x10 = 1000 inner cubes in the cube.
- Each inner cube is formed by the intersection of 8 tiny cubes.
- Since each tiny cube has three colors, each inner cube will have all three colors.
- Therefore, there are 1000 inner cubes in total that have all three colors.
Conclusion:
- From the analysis above, we can conclude that there are 8 corners and 1000 inner cubes in the cube that have all three colors.
- Therefore, the total number of tiny cubes that have all three colors is 8 + 1000 = 1008.
- Option C, 8, is the correct answer.
- The cube is divided into 1728 equal tiny cubes, which means it is a 12x12x12 cube.
- Each face of the cube is varnished with different colors, with two portions having the same color and two portions having different colors.
- We need to determine the number of tiny cubes that will have all three colors.
Solution:
To solve this problem, we need to analyze the different segments of the cube and determine the number of tiny cubes that will have all three colors.
1. Corners:
There are eight corners in the cube: U, V, W, X, Y, Z, A, and B.
- Each corner is formed by the intersection of three faces.
- Since each face has two segments with the same color and two segments with different colors, each corner will have all three colors.
- Therefore, there are 8 corners in total that have all three colors.
2. Edges:
There are 12 edges in the cube.
- Each edge is formed by the intersection of two faces.
- Since each face has two segments with the same color and two segments with different colors, each edge will have two segments with the same color and one segment with a different color.
- Therefore, none of the edges will have all three colors.
3. Faces:
There are 6 faces in the cube.
- Each face is formed by dividing the cube into a 12x12 grid.
- Each face has two segments with the same color and two segments with different colors.
- Each face will have 6 segments with the same color and 6 segments with a different color.
- Therefore, none of the faces will have all three colors.
4. Inner Cubes:
There are (12-2) x (12-2) x (12-2) = 10x10x10 = 1000 inner cubes in the cube.
- Each inner cube is formed by the intersection of 8 tiny cubes.
- Since each tiny cube has three colors, each inner cube will have all three colors.
- Therefore, there are 1000 inner cubes in total that have all three colors.
Conclusion:
- From the analysis above, we can conclude that there are 8 corners and 1000 inner cubes in the cube that have all three colors.
- Therefore, the total number of tiny cubes that have all three colors is 8 + 1000 = 1008.
- Option C, 8, is the correct answer.
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Community Answer
A Cube is segmented into 1728 equal tiny cubes and having corner named...
The number of corners is 8 hence answer for tiny cubes which have all the three colours are related to 8 corners.
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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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer?
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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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about 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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer?.
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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about 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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 two portion with same colour and two with different colour. How many tiny cubes will be formed having all the three colours?a)2b)4c)8d)6Correct answer is option 'C'. Can you explain this answer?.
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