Final answer:
The radius of a circular region with a population of approximately 250,000 and a population density of about 125 people per square mile is approximately 25.2 miles. You calculate this by first determining the area of the region based on population and density, and then using the area to find the radius of the circle.
Step-by-step explanation:
Finding the Radius of a Circular Region Based on Population Density
To find the radius of the circular region based on a population density of 125 people per square mile for an approximate population of 250,000 people, we will use the formula for population density, which is population divided by area. For a circular area, the area A is given by the formula πr², where r is the radius and π (pi) is approximately 3.14159. Therefore, the calculation involves solving for r in the equation 250,000 = 125 * πr².
The first step is to divide the population by the population density to find the area:
Area A = Population / Population Density
A = 250,000 / 125
A = 2,000 square miles
Next, we use the area of a circle formula to find the radius:
πr² = 2,000
r² = 2,000 / π
r = √(2,000 / π)
After calculating the square root, we find that the radius of the circular region is approximately 25.2 miles.