There is a cube in which one pair of adjacent faces is painted Blue, the second
pair of adjacent faces is painted Pink and the third pair of adjacent faces is painted
Black. This cube is now cut into 125 smaller but identical cubes.
Q: How many small cubos do not have any Blue paint on them?
Answers
Answer:
75
Step-by-step explanation:
There are 125 smaller Cubes,
Therefore, n = 5
As we know the general equations are,,
For 3 Faces painted - 8 Cubes (fixed)
For 2 faces painted - (n-2) 12 = 36
For 1 face painted - 6(n-2) ^2 = 54
For 0 face painted - (n-2) ^3 = 27
.
.
Now according to question,
We have to find small cubes that do not have Blue paint on them.
Therefore,
It must be equal to= Total cubes - Cubes painted blue
Now 3 faces painted is fixed = 8
2 faces painted = (n-2) 8 = 24 { There are 12 edges}
3 faces painted = 2(n-2)^2 = 18
Total cubes painted blue = 8+ 24+18 = 50
Therefore, no blue painted = 125-50 = 75
Given:
There is a cube in which one pair of adjacent faces is painted Blue,
the second pair of adjacent faces is painted Pink and
the third pair of adjacent faces is painted Black.
This cube is now cut into 125 smaller but identical cubes.
To Find:
How many small cubes do not have any Blue paint on them.
Solution:
Cube is cut in 125 smaller cubes then,
n³ = 152
n= 5
in bigger cube, each edge is cut in to 5 parts.
and opposite surfaces are painted of same color means there are
2 surface of blue
2 surface of pink
2 surface of black
as each face is cut into 5 layers in which 2 layers are painted.
total cubes = 5 layers x 5 layers x 5 layers
If we remove two layers from any group of 5 layers then we will get the number of those cubes which are not painted from the color of the layer which is removed.
If we remove two layers of black we will get= 3x5x5
=75, these are the cubes which are not painted black
If we remove the two layers of blue , we will get the block which are not painted blue
=3x5x5 = 75
Hence the number of blocks which are not painted blue are 75.