A cube with each edge of 4 cm is painted on all faces. How many of 1 cm cubes,…
20202020
A cube with each edge of 4 cm is painted on all faces. How many of 1 cm cubes, cut out of the larger cube, will not have paint on any of its sides?
- A.
3
- B.
4
- C.
6
- D.
8
Attempted by 94 students.
Show answer & explanation
Correct answer: D
Concept: When a large painted cube is cut into smaller unit cubes, only the cubes lying strictly inside (not touching any outer face) stay unpainted. These inner cubes form a smaller cube called the core.
Formula: Number of unpainted cubes = (n - 2)^3, where n is the number of unit cubes along one edge (Edge of large cube / Edge of small cube).
Given: Edge of the large cube = 4 cm, edge of each small cube = 1 cm.
Step 1 - Find n: n = 4 cm / 1 cm = 4.
Step 2 - Apply the formula: Unpainted cubes = (4 - 2)^3 = 2^3 = 2 x 2 x 2 = 8.
Therefore, exactly 8 of the smaller cubes have no paint on any face. The answer is 8.