The problem in the image asks:

"A cube made of 1,331 small cubes gets a painted surface. Find the number of small unpainted cubes."

To solve this, we first identify the dimensions of the larger cube. Since it is made of 1,331 small cubes, we assume the larger cube has a volume of 1,331 units.

Step 1: Find the side length of the larger cube.

Since the volume of a cube is the cube of its side length, we need to find the cube root of 1,331:

$\text{Side length of the cube} = \sqrt[3]{1331} = 11$

So, the larger cube has dimensions $11 \times 11 \times 11$.

Step 2: Identify the inner unpainted small cubes.

When the surface of the cube is painted, only the outer layers of small cubes are affected. The inner unpainted cubes are the ones that form a smaller cube inside, where each side is reduced by 2 units (since the outer layer is painted from all sides).

Thus, the side length of the inner unpainted cube is: $11 - 2 = 9$

Step 3: Calculate the volume of the inner unpainted cube.

The number of unpainted small cubes is the volume of this inner cube, which is: $9^3 = 729$

Final Answer:

The number of small unpainted cubes is 729.

Would you like further details or clarifications?

Related Questions:

1. What is the total surface area of the larger painted cube?
2. How many cubes are painted on only one face?
3. How many cubes are painted on exactly two faces?
4. What would be the number of unpainted cubes if the larger cube had a side length of 13?
5. How many cubes are fully painted on all three faces at the corners?

Tip:

When working with cube problems, always remember that only the outer layers of the cube are painted, and you can calculate the unpainted cubes by examining the smaller cube left inside after removing the outer layer.