Question

How many cubes having red, green and black colours on at least one side of the cube will be formed?

• A. 16
• B. 8
• C. 4
• D. 12
• E. 24
• A. 24
• B. 12
• C. 64
• D. 20
• J. 6
• A. 4
• B. 8
• C. 12
• D. 16
• O. 20
• A. 4
• B. 8
• C. 12
• D. 16
• T. 10
• A. 8
• B. 12
• C. 16
• D. 20
• Y. 10

Answer 1

The Correct Option is C

Concept: Counting corner cubes with three faces painted.
Step 1: Understand structure.
Cuboid dimensions: 6 × 4 × 1 → divided into 1 cm cubes → total cubes = 24
Step 2: Identify colored faces.
Each pair of opposite faces has a different color: Black (4×1), Red (6×1), Green (6×4)
Step 3: Find cubes with all three colors.
Cubes having red, green and black colors must lie at corners where three differently colored faces meet.
Step 4: Count such cubes.
A cuboid has 8 corners, but since height = 1, only 4 distinct corner cubes exist.
Step 5: Final answer.
Thus, number of cubes having all three colors = 4.

Answer 2

Concept: Number of small cubes = product of dimensions.
Step 1: Use formula.
\[ \text{Number of cubes} = \text{length} \times \text{breadth} \times \text{height} \]
Step 2: Substitute values.
\[ = 6 \times 4 \times 1 = 24 \]
Step 3: Final answer.
Thus, total small cubes formed = 24.

Answer 3

Concept: Counting cubes based on number of painted faces.
Step 1: Understand dimensions.
Cuboid = 6 × 4 × 1 → only one layer in height
Step 2: Key observation.
Since height = 1, each small cube has: - Top face painted (green) - Bottom face painted (green) So each cube already has at least 2 coloured faces.
Step 3: Identify cubes with 4 coloured faces.
Cubes on edges (excluding corners) will have: - Top & bottom (2 faces) - Two side faces (2 more) Total = 4 coloured faces
Step 4: Count such cubes.
There are 4 such edge positions in this flat cuboid.
Step 5: Final answer.
Thus, number of cubes with 4 coloured faces = 4.

Answer 4

Concept: Cubes with exactly two painted faces (green only).
Step 1: Understand structure.
Cuboid = 6 × 4 × 1 → only one layer Top and bottom faces are green → every cube has 2 green faces.
Step 2: Requirement.
We need cubes having: - exactly 2 green faces - no red or black faces
Step 3: Identify valid cubes.
Such cubes must lie strictly inside (not on edges), so they do not touch red/black faces.
Step 4: Count interior cubes.
\[ \text{Interior cubes} = (6 - 2) \times (4 - 2) \] \[ = 4 \times 2 = 8 \]
Step 5: Final answer.
Thus, required cubes = 8.

Answer 5

Concept: Remove cubes having specified colors.
Step 1: Total cubes.
\[ 6 \times 4 \times 1 = 24 \]
Step 2: Key observation.
Top and bottom faces are green → every cube has green color.
Step 3: Interpretation.
If cubes having both black and green colours are removed, only cubes without black remain.
Step 4: Count cubes without black.
Black faces are on $4 \times 1$ sides $\Rightarrow$ these affect 8 cubes. \[ \text{Remaining cubes} = 24 - 8 = 16 \]
Step 5: Final answer.
Thus, number of cubes remaining = 16.