a 3 cm by 3 cm by 3 cm cube is painted all over its outside and is then cut into 27 smaller cubes. How many of these small cubes have paint on more than one face? please explain how you work it out,thanks

any of the smaller cubes on the outside faces and edges will have paint on them

The only ones without any paint will be the single small cube in the middle. So one of them

thanks for your kindness

To determine the number of small cubes with paint on more than one face after cutting the larger cube, we need to visualize the cube and approach the problem step by step.

Step 1: Visualize the larger cube
Consider the 3 cm by 3 cm by 3 cm cube. Each side of the cube has 3 × 3 = 9 unit squares. There are 6 sides in total, so the cube has a total of 6 × 9 = 54 unit squares.

Step 2: Divide the larger cube into smaller cubes
Cutting along each grid line, divide the larger cube into 27 smaller cubes. Each side of the larger cube will be divided into three sections, resulting in a 3 × 3 × 3 grid of smaller cubes.

Step 3: Analyze the smaller cubes
Now, let's examine the smaller cubes that were formed. Recall that each smaller cube has a volume of 1 cm^3 since each dimension measures 1 cm. There is a total of 27 smaller cubes.

Step 4: Identify the cubes with paint on more than one face
To determine which smaller cubes have paint on more than one face, we need to examine each smaller cube and consider how many faces are exposed.

- The smaller cubes at the center of each face will have paint on only one face since all neighboring faces are glued to other cubes.
- The smaller cubes at the corners of the larger cube will have paint on three faces since they are not glued to any other cubes.
- The smaller cubes along the edges will have paint on two faces since they will have one face glued to a neighboring cube.

Step 5: Count the small cubes with paint on more than one face
Remembering the distribution we found in step 4, we can count the cubes as follows:
- There are 8 cubes at the corners, each with paint on three faces.
- There are 12 cubes along the edges, each with paint on two faces.
- The remaining 7 cubes are in the center and have paint on only one face.

Hence, the number of small cubes with paint on more than one face is 8 + 12 = 20.