To calculate the area of a circle, we use the formula:

$\text{Area} = \pi \times r^2$

Here, the diameter $d$ is given as 32 miles. The radius $r$ is half of the diameter:

$r = \frac{d}{2} = \frac{32}{2} = 16 \text{ miles}$

Now, we substitute the radius and $\pi \approx 3.14$ into the formula:

$\text{Area} = 3.14 \times (16)^2 = 3.14 \times 256$

Multiplying:

$\text{Area} = 3.14 \times 256 = 803.84 \text{ square miles}$

So, the area of the circle is approximately 803.84 square miles.

Would you like any further details or explanations?

Here are 5 related questions:

1. What is the circumference of the circle with a diameter of 32 miles?
2. How would the area change if the diameter was doubled?
3. Can you calculate the area if $\pi$ were approximated as 3.1416?
4. How is the formula for the area of a circle derived?
5. What is the area of a semicircle with the same diameter?

Tip: When solving problems involving circles, always remember that the radius is half the diameter.