Question

A cube painted red on two adjecent faces and black on the faces opposite to the red faces and green on the remaining faces is cut into sixty-four smaller cubes of equal size.
1.How many cubes are there which have no face painted?
2.How many cubes have only one face printed?
3. How many cubes have less than three faces painted?
4. How many cubes are there with three faces printed?
5. How many cubes have one face green and one of the adjacent faces black or red?

Please explain with steps.

Answer that I know
1)8
2)24
4)8
​

Answer 1

Answer:

1) 8

2) 24

3) 8

4) 24

5) 16

Step-by-step explanation:

4) total no. of cubes = 64.

number of cubes on each edge painted two sides = 2

total cubes = 2 multiply by 12 = 24.

*HOPE IT HELPS*

Answer 2

Answer:

If the cube is cut into $4\times 4\times 4=64$ small cubes, then 8 cubes  have no face painted, 24 cubes have only one face printed, 56 cubes have less than three faces painted, 8 cubes are there with three faces printed and 24 cubes have one face green and one faces black or red.

Step-by-step explanation:

Given a cube painted red on two adjacent faces, black on the faces opposite to the red faces and green on the remaining faces.

This cube is cut into sixty-four smaller cubes of equal size.

If the cube is cut in 3-dimensions, i.e., $4\times 4\times 4$, then it will make equal 64 small cubes.

1. The big cube have all the faces painted. The small cubes that are inside will have no face painted.

Cube have six faces, if one layer of cubes are removed from each face, then $2\times 2\times 2=8$ will be remaining at the center.

Therefore, the cubes which have no face painted are 8.

2. Cube have six faces, and at each face, 4 cubes have only one side painted.

Hence, $6\times 4=24$ cubes have only one face painted.

3. Only the corner cubes have three faces painted. In a cube there are totally eight corners. so, 8 cubes have three faces painted.

Then the remaining cubes, i.e., $64-8=56$ have less than three faces painted.

4. Only the corner cubes have three faces painted. In a cube there are totally eight corners. so, 8 cubes have three faces painted.

5. The cube have two sides painted with green colour.

    All the edge cubes of each side, i.e., 12 cubes on each side, have a green on one face and black or red on other side.

Therefore, $12\times 2=24$ cubes have one face green and one of the adjacent faces black or red.