To find the radius of the circular region, we need to use the formula for the area of a circle:
A = πr^2
We also know that the population density is 566 people per square mile, which means that there are 566 people in every square mile of the circular region. Therefore, the total population, P, is:
P = 570,000 people
We can use this information to find the area of the circular region:
P = 566 people/mile^2 × A
570,000 people = 566 people/mile^2 × πr^2
πr^2 = 570,000 people / 566 people/mile^2
πr^2 = 1006.34 mile^2
r^2 = 1006.34 mile^2 / π
r^2 = 320.4 mile^2
r = √(320.4 mile^2)
r ≈ 17.9 miles
Rounding to the nearest tenth of a mile, the radius of the circular region is approximately 17.9 miles.