To find the radius of the circle, we can use the formula for the circumference of a circle:

$C = 2 \pi r$

Where:

• $C$ is the circumference
• $r$ is the radius
• $\pi$ is approximately 3.14

Given:

• Circumference $C = 31.4$ miles
• $\pi \approx 3.14$

We can rearrange the formula to solve for the radius $r$:

$r = \frac{C}{2 \pi}$

Substitute the given values:

$r = \frac{31.4}{2 \times 3.14}$

Now, calculate:

$r = \frac{31.4}{6.28} \approx 5$

So, the radius of the circle is approximately 5 miles.

Would you like to go over any part of this process in more detail? Here are some related questions you might find useful:

1. What is the diameter of the circle?
2. How can you calculate the area of the circle using the radius?
3. What would the radius be if the circumference was doubled?
4. How would the formula change if you used a more precise value for $\pi$?
5. Can you calculate the circumference if the radius is 7 miles?

Tip: Always make sure you know what formula to use and the proper rearrangements to solve for the unknown variable!