Question

A cube of side 4 cm is painted on all its faces. If it is sliced into 1 cm cubes, how many 1 cm cubes will have exactly one face painted?

• A. 8
• B. 16
• C. 24
• D. 32

Hint:

For painted cube problems, focus on the inner cubes of each face to count those with exactly one face painte(d)

Answer 1

The Correct Option is C

A cube of side 4 cm is cut into 1 cm cubes, so the number of smaller cubes is \( 4^3 = 64 \). 
To find cubes with exactly one face painted, consider the cubes on each face of the large cube. Each face of the cube has \( 4 \times 4 = 16 \) smaller cubes, but the edge and corner cubes are share(d) 
Cubes with exactly one face painted are those on the surface, excluding edges and corners. For each face: 
Inner cubes = \( (4 - 2) \times (4 - 2) = 2 \times 2 = 4 \). 
There are 6 faces, so total cubes with one face painted = \( 6 \times 4 = 24 \). 
Thus, the answer is 24.