Solution to Painting a Wooden Cube: Counting Smaller Cubes with Exactly Two Red Faces

Imagine a wooden cube with each side measuring 3 inches, painted entirely red on the exterior. If this cube is then cut into smaller cubes, each with a side length of 1 inch, we can explore the number of smaller cubes that will have exactly two red faces.

Setting Up the Problem

The original cube has a volume of:

3 inches × 3 inches × 3 inches 27 cubic inches

This results in:

3 × 3 × 3 27 smaller 1-inch cubes

Finding Smaller Cubes with Exactly Two Red Faces

Cubes with exactly two red faces are found along the edges of the larger cube. Each edge of the original cube will contribute exactly one smaller cube with two red faces. Let's break this down further:

Each edge of the cube is 3 inches and contains 3 smaller cubes. The corner cubes on each edge will have three red faces, and the middle cube on each edge will have exactly two red faces.

Counting the Edges

The original cube has 12 edges. Therefore:

12 edges × 1 middle cube per edge 12 smaller cubes

Conclusion and Additional Insights

Given that the cube is divided into 27 smaller 1-inch cubes, the breakdown is as follows:

8 cubes have three red faces (located at the corners). 12 cubes have exactly two red faces (located along the edges). 6 cubes have one red face (located in the middle of the faces). 1 cube has no face painted (located at the very center of the original cube).

Thus, the final answer is:

12 smaller cubes with exactly two red faces.

SEO Optimized Content

For optimal SEO, ensure that your content is well-structured with H1, H2, and paragraph tags. Use relevant keywords such as wooden cube, red faces, and smaller cubes throughout the text to improve visibility on search engines. Regularly update and maintain high-quality, informative content to attract and retain readers, thereby improving your site's search engine ranking.