A 15 cm colored cube is cut into 3 m small cubes, then how many cubes are formed which have only one face painted?
Answer & explanation
Correct answer: option 1
Given information:
- The original cube has a side length of 15 cm.
- The original cube is cut into 3 cm small cubes.
Step 1: Calculate the number of small cubes in the original 15 cm cube.
Number of small cubes = (15 cm / 3 cm)^3 = 5^3 = 125 small cubes
Step 2: Identify the small cubes that have only one face painted.
The small cubes on the surface of the original cube (excluding the corners) have only one face painted.
Number of small cubes with one face painted = (5 × 5) + (5 × 5) + (5 × 5) - 4 = 70 small cubes.