https://file.aiquickdraw.com/mathbot/file/1727761461851inllvx4d.jpg

We are given a large cube with side length 4 inches. This cube is painted red on all its faces and then cut into 64 smaller cubes, each with side length 1 inch (since \(4^3 = 64\) smaller cubes in total). We are tasked with finding how many of these smaller 1-inch cubes have exactly two red faces.

### Step-by-step solution:

1. **Cube structure**: 
   Since the large cube has 4-inch sides, it is composed of 4 cubes along each edge. After cutting, each small cube is 1 inch in length, and the total number of smaller cubes is \(4^3 = 64\).

2. **Cubes with two red faces**: 
   These are the cubes that are located along the **edges** of the large cube, but not at the corners. Corner cubes have three painted faces, while cubes along the edges but away from the corners have two painted faces.

3. **Number of edge cubes with two painted faces**:
   - Each edge of the large cube consists of 4 smaller cubes.
   - The two corner cubes at each end of an edge have three painted faces.
   - Therefore, the two middle cubes on each edge have exactly two painted faces.

4. **Counting edges**:
   - A cube has 12 edges.
   - On each edge, there are 2 cubes with exactly two painted faces (the middle cubes).
   - Thus, the total number of cubes with two painted faces is:
     \[
     12 \text{ edges} \times 2 \text{ cubes per edge} = 24 \text{ cubes}.
     \]

Therefore, the number of 1-inch cubes that are painted red on exactly two faces is **24**.

### Final Answer: 
The correct answer is **D. 24**.

Would you like further details or have any questions? Here are some related questions for further exploration:

1. How many of the small cubes have exactly one face painted red?
2. How many of the small cubes have no faces painted red?
3. How many of the small cubes have exactly three faces painted red?
4. If the large cube was painted in a different color on each face, how would the answer change?
5. What is the total surface area of all the small cubes that have at least one face painted red?

**Tip**: When analyzing painted cubes, always think about the geometry of corners, edges, and faces to categorize cubes by the number of painted faces.

A cube 4 inches on each side is painted red and cut into 64 1-inch cubes. How many 1-inch cubes are painted red on two faces only?

This problem asks how many 1-inch cubes, out of 64 smaller cubes formed by cutting a 4-inch painted cube, have exactly two faces painted red. The solution involves understanding cube geometry, including edges and face coverage. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation