Two opposite faces of a big cube are painted with red colour, two adjacent…
2021
Two opposite faces of a big cube are painted with red colour, two adjacent faces are painted with yellow colour and remaining faces are painted with blue colour. 4 equal cuts are made on each edge of this big cube and some small cubes are obtained. How many small cubes will have one face painted with blue colour and one face painted with yellow colour?
- A.
2
- B.
4
- C.
16
- D.
10
Attempted by 19 students.
Show answer & explanation
Correct answer: D
1. Calculate parts per edge ($n$): 4 cuts mean $n = 4 + 1 = 5$ parts per edge.
2. Map the colors: Top/Bottom = Red (opposite), Front/Right = Yellow (adjacent), Back/Left = Blue (adjacent).
3. Find intersections: Blue and Yellow faces meet at exactly 2 edges (Front-Left edge and Right-Back edge).
4. Count the cubes: The question asks for cubes with a blue and a yellow face, which includes both middle-edge cubes and corner cubes. Since there are $n=5$ cubes along each of the 2 edges, the total is $2 \times 5 = 10$ cubes.
Final Answer: Option D