https://file.aiquickdraw.com/mathbot/file/1728933472704maci27re.jpg

To solve the problem, let's determine the ratio between the circumferences of Circle A and Circle B.

### Step-by-Step Solution:
1. **Circumference Formula**:
   The circumference \( C \) of a circle is given by:
   \[
   C = 2 \pi r
   \]
   where \( r \) is the radius.

2. **Find the Circumference of Each Circle**:
   - **Circle A** has a radius of 8 inches:
     \[
     C_A = 2 \pi \times 8 = 16 \pi \, \text{inches}
     \]
   - **Circle B** has a radius of 4 inches:
     \[
     C_B = 2 \pi \times 4 = 8 \pi \, \text{inches}
     \]

3. **Calculate the Ratio**:
   The ratio of the circumferences is:
   \[
   \frac{C_A}{C_B} = \frac{16 \pi}{8 \pi} = 2
   \]

### Final Answer:
The ratio of the circumferences of Circle A to Circle B is \(\boxed{2}\).

Would you like more details on any of these steps? Here are some follow-up questions for further practice:

1. What is the area of each circle, and how does the ratio of their areas compare to the ratio of their circumferences?
2. How would the ratio change if the radius of Circle B were increased to 6 inches?
3. What is the diameter of each circle, and how do the diameters relate to the circumferences?
4. How does the ratio of circumferences change if both radii are doubled?
5. What is the formula for the circumference of a circle, and how is it derived?

**Tip:** When comparing measurements like circumference or area of similar shapes, remember that linear dimensions (like circumference) scale directly with the change in radius, while area scales with the square of the radius change.

The two circles shown above have radii of 8 in. and 4 in. What is the ratio of the circumference of Circle A to the circumference of Circle B?

Learn how to calculate the ratio of the circumferences of two circles with radii of 8 inches and 4 inches. This geometry problem explores the formula for circumference and how ratios apply to similar figures. Ideal for students in Grades 6-8.

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