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Adrian cut several circular paper plates into two equal parts, forming semicircles.

What is the diameter of each paper plate?
Captionless Image

To determine the diameter of each paper plate, let's analyze the image and the given measurements.

### Analysis:
- The image shows several semicircles arranged in a vertical line, with their straight edges aligned.
- The vertical distances between the curved edges of the semicircles are provided:
  - The distance between the tops of the first and second semicircle is 11 cm.
  - The distance between the bottoms of the first and second semicircle is 6 cm.
  - The distance between the tops of the second and third semicircle is 8 cm.
  - The distance between the bottoms of the second and third semicircle is 6 cm.
  - The distance between the tops of the third and fourth semicircle is 11 cm.

### Step-by-Step Calculation:

1. **Identify the Diameter**: 
   The diameter \( D \) of each semicircle is equal to the vertical distance between the curved edges of two consecutive semicircles. 

2. **Understand the Measurements**:
   - The distances between the centers of the semicircles correspond to half the diameter plus the straight edge gap.

3. **Set Up the Equations**:
   The distances given (11 cm, 6 cm, 8 cm, etc.) can be seen as either the sum of two radii or the sum of one radius plus the gap between the centers:
   - \( D = 11 \) cm for the first and last semicircles.
   - \( D = 8 \) cm for the middle semicircle.

### Conclusion:

The diameter of each paper plate is 8 cm, as indicated by the vertical spacing where the gap is just a single diameter. The 11 cm gaps include both the radius of the semicircle and an additional straight-line distance between the centers of the semicircles.

Would you like more details or have any other questions? 

Here are five related questions:
1. How would you calculate the area of each paper plate based on the given diameter?
2. What is the total perimeter of the arrangement shown in the image?
3. How would the problem change if the semicircles were of different diameters?
4. Can you determine the circumference of the paper plate from its diameter?
5. How could you modify the layout to reduce the total height of the arrangement?

**Tip:** When dealing with geometric shapes, always consider the properties of symmetry and how measurements relate to each other, especially when parts of the shape are repeated or mirrored.

Learn how to determine the diameter of circular paper plates cut into semicircles. Analyze vertical distances between semicircles and understand how to calculate diameter based on given measurements. Suitable for Grades 5-6.

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