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About 19,400 people live in a circular region with a 5-mile radius. Find the population density in people per square mile.
A
about 237 people per square mile
B
about 247 people per square mile
C
about 257 people per square mile
D
about 267 people per square mile



Answer :

GinnyAnswer
To find the population density in people per square mile for the circular region, we need to follow these steps:

1. Calculate the area of the circular region.
2. Divide the population by the area to find the population density.

Let's start by calculating the area of the circular region using the formula for the area of a circle: [tex]\( A = \pi r^2 \)[/tex], where [tex]\( A \)[/tex] is the area and [tex]\( r \)[/tex] is the radius of the circle.

Given that the radius [tex]\( r \)[/tex] is 5 miles, the area [tex]\( A \)[/tex] will be:

[tex]\[ A = \pi \times (5\text{ miles})^2 \][/tex]
[tex]\[ A = \pi \times 25\text{ square miles} \][/tex]
[tex]\[ A = 25\pi\text{ square miles} \][/tex]

Next, we'll compute the population density ([tex]\( D \)[/tex]) by dividing the population by the area:

[tex]\[ D = \text{population} / \text{area} \][/tex]
[tex]\[ D = 19400 \text{ people} / 25\pi \text{ square miles} \][/tex]

Now, we need to perform this calculation. The value of [tex]\( \pi \)[/tex] is approximately 3.14159.

So:
[tex]\[ D \approx 19400\text{ people} / (25 \times 3.14159)\text{ square miles} \][/tex]
[tex]\[ D \approx 19400\text{ people} / 78.53975\text{ square miles} \][/tex]
[tex]\[ D \approx 247.05\text{ people per square mile} \][/tex]

Rounding this to the nearest whole number results in 247 people per square mile. Therefore, the closest option is:

B about 247 people per square mile
Kendricksmith648
To find the population density in people per square mile, we first need to find the area of the circular region, and then divide the population by that area.

The area of a circle is given by the formula: \( \pi \times \text{radius}^2 \).

Given that the radius is 5 miles, the area of the circular region is:

\[ \pi \times 5^2 = 25\pi \text{ square miles} \]

Now, we divide the population (19,400 people) by the area:

\[ \text{Population density} = \frac{\text{Population}}{\text{Area}} = \frac{19,400}{25\pi} \approx \frac{19,400}{25 \times 3.14} \approx \frac{19,400}{78.5} \approx 247 \text{ people per square mile} \]

So, the correct answer is:

B) about 247 people per square mile

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