A cube is colored orange on one face, pink on the opposite face, green on one…
2018
A cube is colored orange on one face, pink on the opposite face, green on one face and silver on the remaining faces. This cube is now cut into 125 smaller cubes of equal size. How many smaller cubes have at most two faces colored?
- A.
125
- B.
121
- C.
117
- D.
123
Attempted by 7 students.
Show answer & explanation
Correct answer: C
To determine the number of smaller cubes with "at most two faces colored," we first analyze the structure of the 5 × 5 × 5 cube.
Step-by-Step Analysis
Understand the total: The large cube is cut into 125 smaller cubes (5 × 5 × 5 = 125).
Identify cubes with more than two faces colored:
In a standard cube cut, only the corner cubes have three faces exposed on the outside.
A cube has 8 corners, meaning 8 smaller cubes have three faces colored.
Apply the "at most two" condition:
"At most two" means cubes with 0, 1, or 2 faces colored.
This is equivalent to taking the total number of cubes and subtracting those that have more than two faces colored.
Total cubes (125) - Cubes with 3 faces colored (8) = 117.