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A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.
- a)1 : 4
- b)1 : 3
- c)1 : 2
- d)2 : 3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A cube of side 3 units is formed using a set of smaller cubes of side ...
Total number of cubes = 9 × 3 = 27
∴Total number of faces = 27 × 6 = 162
∴Total number of non-visible faces = 162 - 54 = 108
∴Total number of faces = 27 × 6 = 162
∴Total number of non-visible faces = 162 - 54 = 108
∴ Number of visible faces / Number of non visible faces = 54/108 = 1/2
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A cube of side 3 units is formed using a set of smaller cubes of side ...
Understanding the Problem
To solve this problem, we first need to visualize the setup. A cube with a side length of 3 units consists of smaller cubes, each with a side length of 1 unit.
Calculating the Number of Smaller Cubes
- The total number of smaller cubes in the larger cube is:
- Volume of larger cube = 3^3 = 27
- Therefore, there are 27 smaller cubes (1 unit each).
Faces of Smaller Cubes
- Each smaller cube has 6 faces.
- Total faces of all smaller cubes = 27 * 6 = 162 faces.
Visible Faces Calculation
- To determine the number of visible faces, we need to analyze the arrangement of the smaller cubes in the larger cube.
- The cubes on the surface of the larger cube are the ones whose faces are visible.
Identifying Visible Faces
- The cubes on the corners contribute 3 visible faces each (8 corners).
- The cubes on the edges contribute 2 visible faces each (12 edges, 1 cube per edge).
- The cubes on the faces contribute 1 visible face each (6 faces, 1 cube per face).
- By careful counting:
- Corner cubes = 8 cubes * 3 faces = 24 visible faces
- Edge cubes = 12 cubes * 2 faces = 24 visible faces
- Face cubes = 6 cubes * 1 face = 6 visible faces
- Total visible faces = 24 + 24 + 6 = 54 faces.
Calculating Non-visible Faces
- Total faces = 162 (calculated previously).
- Non-visible faces = Total faces - Visible faces = 162 - 54 = 108 faces.
Finding the Proportion
- Proportion of visible to non-visible faces = 54 : 108 = 1 : 2.
Thus, the correct answer is option 'C': 1 : 2.
To solve this problem, we first need to visualize the setup. A cube with a side length of 3 units consists of smaller cubes, each with a side length of 1 unit.
Calculating the Number of Smaller Cubes
- The total number of smaller cubes in the larger cube is:
- Volume of larger cube = 3^3 = 27
- Therefore, there are 27 smaller cubes (1 unit each).
Faces of Smaller Cubes
- Each smaller cube has 6 faces.
- Total faces of all smaller cubes = 27 * 6 = 162 faces.
Visible Faces Calculation
- To determine the number of visible faces, we need to analyze the arrangement of the smaller cubes in the larger cube.
- The cubes on the surface of the larger cube are the ones whose faces are visible.
Identifying Visible Faces
- The cubes on the corners contribute 3 visible faces each (8 corners).
- The cubes on the edges contribute 2 visible faces each (12 edges, 1 cube per edge).
- The cubes on the faces contribute 1 visible face each (6 faces, 1 cube per face).
- By careful counting:
- Corner cubes = 8 cubes * 3 faces = 24 visible faces
- Edge cubes = 12 cubes * 2 faces = 24 visible faces
- Face cubes = 6 cubes * 1 face = 6 visible faces
- Total visible faces = 24 + 24 + 6 = 54 faces.
Calculating Non-visible Faces
- Total faces = 162 (calculated previously).
- Non-visible faces = Total faces - Visible faces = 162 - 54 = 108 faces.
Finding the Proportion
- Proportion of visible to non-visible faces = 54 : 108 = 1 : 2.
Thus, the correct answer is option 'C': 1 : 2.
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A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer?.
A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer?.
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A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.a)1 : 4b)1 : 3c)1 : 2d)2 : 3Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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