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The problem is asking to find the width and thickness of a carbon brush that is entirely enveloped by a 0.406 mm thick copper plate.

### Given:
- The **outer width** (total width) is 38.9 mm.
- The **outer thickness** is 19.17 mm.
- The **thickness of the copper plating** is 0.406 mm on all sides.

### To solve:
1. **Width of the carbon brush (inner width)**:
   Since the copper plating surrounds the brush on both sides, we need to subtract twice the thickness of the copper from the total width:
   \[
   \text{Inner width} = 38.9 \, \text{mm} - 2 \times 0.406 \, \text{mm}
   \]
   \[
   \text{Inner width} = 38.9 \, \text{mm} - 0.812 \, \text{mm} = 38.088 \, \text{mm}
   \]

2. **Thickness of the carbon brush (inner thickness)**:
   Similarly, for the thickness:
   \[
   \text{Inner thickness} = 19.17 \, \text{mm} - 2 \times 0.406 \, \text{mm}
   \]
   \[
   \text{Inner thickness} = 19.17 \, \text{mm} - 0.812 \, \text{mm} = 18.358 \, \text{mm}
   \]

### Final answer:
- **Width of the carbon brush**: 38.088 mm
- **Thickness of the carbon brush**: 18.358 mm

Would you like further clarification or additional details on any step? 

Here are some related questions to practice:
1. What would be the thickness if the copper layer was 0.5 mm thick?
2. How would you calculate the volume of the carbon brush?
3. How much copper is used in terms of volume for this brush?
4. How does changing the copper thickness impact the overall brush dimensions?
5. If the outer width were reduced to 37 mm, what would be the new width of the carbon brush?

**Tip**: Always double-check if the plating or coating is applied on all sides or only some sides for dimension calculations!

Une brosse de carbone est enveloppée entièrement de tous les côtés d'une plaque de cuivre de 0.406 mm d'épaisseur. Trouver la largeur et l'épaisseur de la brosse de carbone.

Learn how to find the inner width and thickness of a carbon brush entirely enclosed in a 0.406 mm copper plating. The problem involves subtracting the copper thickness from the outer dimensions of the brush. This problem is suitable for students in Grades 9-12.

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