Question

A cube is painted on its 3 adjacent faces and cut into 125 small cube the number of cubes with at least 2 faces painted

Answer 1

Answer:

13

Step-by-step explanation:

The cube is cut into 125 small and equal cube pieces.

So each edge should be cut into 5 pieces. [Cube root of 125 is 5.]

And each face should be cut into 25 pieces.

Consider one face among the painted.

It is given in the question that 3 adjacent faces are painted. So assume that its right and bottom faces are also painted.

In the selected face, the bottom left corner is painted on 2 sides, i.e., on its bottom and front sides. Its left side is not painted.

In the selected face, the bottom 3 edge pieces are also painted by 2 sides; on its front and bottom.

In the selected face, the left 3 edge pieces are painted only on 1 side; on its front. So they can't be taken.

The top left corner in the selected face is also painted only on 1 side. So it can't also be taken. The top 3 edge pieces also.

But the top right corner is painted on 2 sides; on its front and right. So it can be taken.

The right 3 edge pieces can also be taken. They're painted on its front and right sides.

The bottom right corner is painted on all its 3 sides. It can also be taken as the question only asks the no. of cubes 'at least' 2 faces painted.

So we got 1 + 3 + 1 + 3 + 1 = 9 pieces.

Now consider the right painted face of the selected.

In this face, also 9 pieces are painted at least 2 faces. But we found 5 among these earlier. Those are, top left corner, 3 left edge pieces, and bottom left corner.

The remaining 4 are the bottom 3 edge pieces and bottom right corner.

So add these to it, and we get 9 + 4 = 13.

Okay. Let's have a look at the bottom painted face.

We don't need to check this face, because all the 9 painted pieces in this face are already found!

So the answer is 13.

Okay, let me prefer a simple method to get the answer.

If a cube is painted on its 3 adjacent faces and cut into 'n^3' small cubes, then the no. of cube pieces with at least 2 faces painted is,

3n - 2.

Here,

n^3 = 125

n = cube root of 125 = 5

3n - 2

3 × 5 - 2

15 - 2

13

So we can find the answer quickly by applying this algebraic equation when such questions are asked.

Hope this may be helpful.

Please mark my answer as the brainliest if this may be helpful.

If I'm saying too much and it's fleeing you more, then sorry for it.

Thank you. Have a nice day.

#adithyasajeevan