A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each. Find the number of smaller cube having all the three faces painted.

Question

Question

This question was previously asked in

SSC CGL 2021 Tier-I (Held On : 12 April 2022 Shift 2)

Answer 1

A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each.

F1 Savita SSC 17-6-22 D38

F1 Savita SSC 17-6-22 D39

All corner cubes are painted on three sides there are 8 corners in cubes.

So, cubes with paint on 3 sides = 8

Hence, "8" is the correct answer.

Additional Information

If a cube has been painted red, blue, and black on pairs of opposite faces and divide it into X parts.

1) Total number of cubes = X³

2) Cubes that have three faces painted = 8 (Because there are only 8 corners in the cube)

3) Cubes which has only two faces painted = (X - 2) × No of Edges (12)

4) Cubes that have only one face painted = (X - 2)² × 6

5) Cubes that have no face painted = (X - 2)³