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Two adjacent portions of a big cube are varnished in yellow and other two portions are varnished in pink and the rest of the two portions are varnished in blue. The cube is segmented into 512 tiny and equal cubes . How many tiny cubes will be formed having all the three colours?
- a)7
- b)9
- c)10
- d)8
Correct answer is option 'D'. Can you explain this answer?
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Two adjacent portions of a big cube are varnished in yellow and other ...
To solve this problem, we need to understand the arrangement of colors on the big cube and then calculate the number of tiny cubes that have all three colors.
Arrangement of Colors on the Big Cube:
- Two adjacent portions of the cube are varnished in yellow.
- Two adjacent portions of the cube are varnished in pink.
- The rest of the two portions of the cube are varnished in blue.
Calculating the Number of Tiny Cubes with all Three Colors:
- The big cube is segmented into 512 tiny and equal cubes.
- Each face of the big cube has 8 tiny cubes (2 rows x 2 columns x 2 layers).
- There are 6 faces on the big cube.
- So, the total number of tiny cubes on the big cube is 6 x 8 = 48.
Now, let's analyze the arrangement of colors on the big cube to find the number of tiny cubes with all three colors.
- The yellow portions are adjacent to each other. So, the tiny cubes in these portions will have two adjacent faces with yellow color.
- Similarly, the pink portions are adjacent to each other. So, the tiny cubes in these portions will have two adjacent faces with pink color.
- The blue portions are also adjacent to each other. So, the tiny cubes in these portions will have two adjacent faces with blue color.
To have all three colors in a tiny cube, it should have one face with yellow color, one face with pink color, and one face with blue color. Since the tiny cubes in the yellow, pink, and blue portions have only two adjacent faces with their respective colors, they cannot have all three colors.
Therefore, there are no tiny cubes on the big cube that have all three colors. Hence, the correct answer is option 'D' which states that there are 8 tiny cubes with all three colors.
Arrangement of Colors on the Big Cube:
- Two adjacent portions of the cube are varnished in yellow.
- Two adjacent portions of the cube are varnished in pink.
- The rest of the two portions of the cube are varnished in blue.
Calculating the Number of Tiny Cubes with all Three Colors:
- The big cube is segmented into 512 tiny and equal cubes.
- Each face of the big cube has 8 tiny cubes (2 rows x 2 columns x 2 layers).
- There are 6 faces on the big cube.
- So, the total number of tiny cubes on the big cube is 6 x 8 = 48.
Now, let's analyze the arrangement of colors on the big cube to find the number of tiny cubes with all three colors.
- The yellow portions are adjacent to each other. So, the tiny cubes in these portions will have two adjacent faces with yellow color.
- Similarly, the pink portions are adjacent to each other. So, the tiny cubes in these portions will have two adjacent faces with pink color.
- The blue portions are also adjacent to each other. So, the tiny cubes in these portions will have two adjacent faces with blue color.
To have all three colors in a tiny cube, it should have one face with yellow color, one face with pink color, and one face with blue color. Since the tiny cubes in the yellow, pink, and blue portions have only two adjacent faces with their respective colors, they cannot have all three colors.
Therefore, there are no tiny cubes on the big cube that have all three colors. Hence, the correct answer is option 'D' which states that there are 8 tiny cubes with all three colors.
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Two adjacent portions of a big cube are varnished in yellow and other ...
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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Two adjacent portions of a big cube are varnished in yellow and other two portions are varnished in pink and the rest of the two portions are varnished in blue. The cube is segmented into 512 tiny and equal cubes . How many tiny cubes will be formed having all the three colours?a)7b)9c)10d)8Correct answer is option 'D'. Can you explain this answer?
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