Question

If a cube, which is painted on five faces, is cut into 27 identical cubes, what is the ratio of the number of unpainted faces to that of the painted faces?​

Answer 1

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A cube painted yellow on all its faces is then cut into 27 smaller cubes of identical sizes. How many cubes are painted on one face only?

Which is the best cement for building your home?

Answer is 6

Here the painted cube is cut into 27 equal-size smaller cubes. So it has been cut into a 3 * 3 * 3 arrangement and the image that comes to mind is a Rubik's cube.

There is 1 cube in the very center (middle of 3 in each axis direction -- pitch, roll, and yaw), so 1 cube has no paint.

On each of the 6 sides of the cube, there is a central smaller cube that is painted once.

Also on each of the 6 sides of the cube, there are 4 cubes (at the middle of the edges). These are shared with one other side of the cube (or we could just count the 12 edge lines -- 12). So, 6 * 4 / 2, or just 12, smaller cubes are painted on 2 edges.

That leaves the 8 corners of the original cube, which are painted on 3 surfaces.

1 (no paint) + 6 (painted 1) + 12 (painted 2) + 8 (painted 3) = 27 total

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Answer 2

Step-by-step explanation:

A cube painted yellow on all its faces is then cut into 27 smaller cubes of identical sizes. How many cubes are painted on one face only?

Which is the best cement for building your home?

Answer is 6

Here the painted cube is cut into 27 equal-size smaller cubes. So it has been cut into a 3 * 3 * 3 arrangement and the image that comes to mind is a Rubik's cube.

There is 1 cube in the very center (middle of 3 in each axis direction -- pitch, roll, and yaw), so 1 cube has no paint.

On each of the 6 sides of the cube, there is a central smaller cube that is painted once.

Also on each of the 6 sides of the cube, there are 4 cubes (at the middle of the edges). These are shared with one other side of the cube (or we could just count the 12 edge lines -- 12). So, 6 * 4 / 2, or just 12, smaller cubes are painted on 2 edges.

That leaves the 8 corners of the original cube, which are painted on 3 surfaces.

1 (no paint) + 6 (painted 1) + 12 (painted 2) + 8 (painted 3) = 27 total

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