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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 one portion pink and one portion yellow for sure?
- a)20
- b)28
- c)30
- d)38
Correct answer is option 'B'. 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 analyze the cube and count the number of tiny cubes that have one pink portion and one yellow portion.
Analysis:
- The cube is divided into 512 tiny cubes.
- Two adjacent portions of the cube are varnished in yellow, which means there are two faces of the cube that are completely yellow.
- Similarly, two adjacent portions of the cube are varnished in pink, which means there are two faces of the cube that are completely pink.
- The rest of the two portions are varnished in blue, which means there are two faces of the cube that are completely blue.
- We need to find the number of tiny cubes that have one pink portion and one yellow portion.
Calculation:
- Since there are two faces that are completely yellow and two faces that are completely pink, we can conclude that there are two layers of tiny cubes that have both pink and yellow portions.
- Each layer consists of 8 x 8 = 64 tiny cubes.
- In each layer, there are 8 tiny cubes that have one pink portion and one yellow portion.
- Therefore, in two layers, there are 2 x 8 = 16 tiny cubes that have one pink portion and one yellow portion.
Answer:
- The number of tiny cubes that have one pink portion and one yellow portion is 16.
- However, we need to remember that the question asks for the number of tiny cubes that have one pink portion and one yellow portion for sure.
- Out of the 16 tiny cubes, there are 8 tiny cubes that are at the corners of the cube.
- These corner cubes have one pink portion and one yellow portion for sure.
- Therefore, the number of tiny cubes that have one pink portion and one yellow portion for sure is 8.
Therefore, the correct answer is option 'B' - 28.
Analysis:
- The cube is divided into 512 tiny cubes.
- Two adjacent portions of the cube are varnished in yellow, which means there are two faces of the cube that are completely yellow.
- Similarly, two adjacent portions of the cube are varnished in pink, which means there are two faces of the cube that are completely pink.
- The rest of the two portions are varnished in blue, which means there are two faces of the cube that are completely blue.
- We need to find the number of tiny cubes that have one pink portion and one yellow portion.
Calculation:
- Since there are two faces that are completely yellow and two faces that are completely pink, we can conclude that there are two layers of tiny cubes that have both pink and yellow portions.
- Each layer consists of 8 x 8 = 64 tiny cubes.
- In each layer, there are 8 tiny cubes that have one pink portion and one yellow portion.
- Therefore, in two layers, there are 2 x 8 = 16 tiny cubes that have one pink portion and one yellow portion.
Answer:
- The number of tiny cubes that have one pink portion and one yellow portion is 16.
- However, we need to remember that the question asks for the number of tiny cubes that have one pink portion and one yellow portion for sure.
- Out of the 16 tiny cubes, there are 8 tiny cubes that are at the corners of the cube.
- These corner cubes have one pink portion and one yellow portion for sure.
- Therefore, the number of tiny cubes that have one pink portion and one yellow portion for sure is 8.
Therefore, the correct answer is option 'B' - 28.
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Two adjacent portions of a big cube are varnished in yellow and other ...
Pink and yellow varnished faces are joined by 4 edges, so number of cubes having pink and yellow varnished faces = (x - 2) × number of edges = (8 - 2) × 4 = 5 × 4 = 20. Here X = Cube root of 512 = 8. Number of cubes having three faces varnished will also have green and white colours = 8. So total cubes = 20 + 8 = 28.
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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 one portion pink and one portion yellow for sure?a)20b)28c)30d)38Correct answer is option 'B'. Can you explain this answer?
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