Question

A cuboid-shaped wooden block has dimensions 6 cm \(\times\) 4 cm \(\times\) 1 cm.
\(\bullet\) The two 4 cm \(\times\) 1 cm faces are coloured black.
\(\bullet\) The two 6 cm \(\times\) 1 cm faces are coloured red.
\(\bullet\) The two 6 cm \(\times\) 4 cm faces are coloured green.
The block is cut into small cubes of side 1 cm.
Question: How many cubes having red, green, and black colours on at least one side of the cube will be formed?

• A. 16
• B. 12
• C. 10
• D. 4

Hint:

For a single-layer cuboid (\(L \times W \times 1\)), the cubes with 3 colors are always the 4 corner cubes. No other cubes can touch the "end" (Black) and "side" (Red) faces simultaneously.

Answer 1

The Correct Option is D

Concept: When a cuboid is cut into 1 cm cubes, the cubes that touch three different colored faces are located at the corners of the original cuboid.

Step 1: Visualizing the cuboid structure.
The dimensions are 6 (length) \(\times\) 4 (width) \(\times\) 1 (height). Since the

height is only 1 cm, it is a "single-layer" block. Every single 1 cm cube cut from this block will have a Green top and a Green bottom.

Step 2: Finding the intersection of three colors.
For a cube to have

Red, Green, and Black: It must be at the point where the Red side, Black side, and Green top meet. These points are the

corners of the block. A cuboid has 8 corners. However, because the height is only 1 cm, the "top corner" and "bottom corner" are part of the

same 1 cm cube. There are only 4 such corner cubes in this single-layer block.