Let's do this question, a cube of side five centimeter is painted on all its faces if it is sliced
into one cubic meter cubes.
How many one cubic meter cubes will have exactly one of their faces painted.
All right.
Pause the video, give it a try, and then let's do it together.
All right.
Let's do it over here.
The side of the cube is five centimeters, right.
So if you slice it into one centimeter cube cubes, how many such cubes will you get?
You will get five to five in the five.
That's equal to six.
Twenty five cubes.
Right.
Over here.
Say, this is the cube that we started with where the site is five centimeter.
All right, so it's sliced in two cubes where the side is one centimeter, but this is five centimeters,
so I need to cut it like this.
All right, so this one, two, three or five men are learning to do the same thing over here.
All right, and the same thing over here as well.
That's how it will look, right?
And it will come over here as well.
And this may also.
OK, so this is how it will look after you slice it up, so we will get five into five into five, that's
equal to six hundred and twenty five cubes.
Now, the question says we need to find out how many cubes will have exactly one of their faces painted.
Now, can you tell me which cubes will have three of their sides painted like these corner cubes?
For example, over here you have a cube at the corner.
Right.
So this part would be painted, this part would be painted and this part would be painted.
Right.
So you can see that in the corners, the cube will be painted in three sides, right to the corner.
Cubes will be painted in three sides.
What about the edge cubes, for example?
Let's take this cube.
So it's not a corner cube, but it is on the edge.
You can see that for this cube, two sides will be painted, right.
This side will be painted and the side will be painted.
So for edge cubes other than corner cubes, two sides will be painted right now.
Let me draw this surface over here like this.
Right.
And these are the corner cubes and these are the edge cubes right now.
You can see that on each face, the remaining three into three cubes.
Right.
So if you remove the edge cubes, right, these you are removing, you will get one, two, three.
Right.
One, two, three.
That's three into three cubes that you have over here.
Right.
So that's one, two, three, and one, two, three over here now on each face, the remaining three
into three cubes will have exactly one side painted, right.
So in one phase, you will get how many such cubes?
Nine.
Three in the tree.
And how many faces do you have?
You have six faces right there.
Therefore, the answer to this question is three into three into six.
That's equal to fifty four cubes.
So that is option C over here.