In an 4 by 5 by 8 unit rectangular prism is painted green on all faces, then cut into cubes. There are 160 cubes How many cubes have at least one face that is painted green

To determine how many of the 160 cubes have at least one face painted green, let's follow these steps:

1. **Calculate the volume and the number of small cubes**:
   - The original rectangular prism has dimensions 4 units by 5 units by 8 units.
   - The volume of the prism is \( 4 \times 5 \times 8 = 160 \) cubic units.
   - Since the prism is cut into 160 cubes, each cube is \( 1 \times 1 \times 1 \) unit in dimension.

2. **Identify the cubes that do not have any painted faces**:
   - To find the cubes that do not have any painted faces, consider the cubes that are entirely inside the prism, not touching any of the outer faces.
   - These inner cubes form a smaller rectangular prism, excluding the outer layer of cubes. This smaller prism will have dimensions reduced by 2 units on each dimension (one unit for each side of a dimension).
   - Dimensions of the inner rectangular prism: \( (4-2) \times (5-2) \times (8-2) = 2 \times 3 \times 6 \).

3. **Calculate the number of inner cubes**:
   - The volume of this inner rectangular prism is \( 2 \times 3 \times 6 = 36 \) cubes.

4. **Subtract the number of inner cubes from the total number of cubes**:
   - Total number of cubes = 160.
   - Number of inner cubes = 36.
   - Number of cubes with at least one face painted = Total cubes - Inner cubes.
   - \( 160 - 36 = 124 \).

Therefore, the number of cubes that have at least one face painted green is \( \boxed{124} \).

Would you like more details or have any questions about this solution? 

Here are 5 more questions you might be interested in:

1. How many edges does a rectangular prism have?
2. What is the surface area of the original rectangular prism?
3. How do you calculate the volume of a cylinder?
4. What is the Pythagorean theorem and how is it used in geometry?
5. How do you find the area of a triangle given its base and height?

**Tip:** When tackling geometric problems, visualizing or sketching the shapes involved can significantly aid in understanding and solving the problem accurately.

Learn how to calculate the number of cubes with at least one face painted green in a rectangular prism. Follow a step-by-step solution involving geometric concepts and volume calculations. Suitable for students in Grades 7-9.

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