Question

In a circular region with a population density of 6480 people per square mile, approximately 860,000 people reside. Determine the radius of the region.

Answer 1

To find the radius of the region, divide the total population by the population density to find the area, then use the formula for the area of a circle to solve for the radius, which is approximately 6.51 miles.

Step-by-step explanation:

To determine the radius of the circular region with a population density of 6480 people per square mile and a total population of approximately 860,000, we can use the formula for population density, which is population divided by area. First, we calculate the area required to hold 860,000 people at a density of 6480 people per square mile:

1. Divide the total population by the population density to find the area: 860,000 people / 6480 people per square mile = 132.716049 square miles.
2. Since the region is circular, the area can also be calculated using the formula for the area of a circle, A = πr2, where r is the radius. We can set this equal to the area we found and solve for r.
3. To solve for r, we need to take the square root of the area divided by π. Therefore, r = √(132.716049 / π) = 6.5056 miles approximately.

Thus, the radius of the circular region is approximately 6.51 miles.