Question

512 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have at most two faces painted?
Select one:
a. 38
b. 36
c. 64
d. 512

Answer 1

Thus there are 72 cubes with two faces painted.

Explanation:

We are given that:

• Number of identical cubes = 512
• Number of faces of cubes = 6

Solution:

Cubes with 1 face painted:

No. of smaller cubes with 1 face painted = 6 × (n-2)² = 6 × (8-2)² = 6 × 36 = 216

2. Cubes with 2 faces painted:

No. of smaller cubes with two faces painted = 12 × (n - 2) = 12 × (8 - 2) = 12 × 6 = 72