QuestionDecember 13, 2025

2. A circular region has a population of about 39,400 and a population density of 230 people per square kilometer.Find the radius of the region.

2. A circular region has a population of about 39,400 and a population density of 230 people per square kilometer.Find the radius of the region.
2. A circular region has a population of about 39,400
and a population density of 230 people per square
kilometer.Find the radius of the region.

Solution
4.0(295 votes)

Answer

7.39\ \text{km} Explanation 1. Write the area formula using population density \text{Area} = \frac{\text{Population}}{\text{Density}} 2. Calculate the area \text{Area} = \frac{39,400}{230} = 171.304\ \text{km}^2 3. Relate area to radius of a circle \text{Area} = \pi r^2 \implies r = \sqrt{\frac{\text{Area}}{\pi}} 4. Solve for the radius r = \sqrt{\frac{171.304}{\pi}} \approx \sqrt{54.56} \approx 7.39\ \text{km}

Explanation

1. Write the area formula using population density<br /> $ \text{Area} = \frac{\text{Population}}{\text{Density}} $<br />2. Calculate the area<br /> $ \text{Area} = \frac{39,400}{230} = 171.304\ \text{km}^2 $<br />3. Relate area to radius of a circle<br /> $ \text{Area} = \pi r^2 \implies r = \sqrt{\frac{\text{Area}}{\pi}} $<br />4. Solve for the radius<br /> $ r = \sqrt{\frac{171.304}{\pi}} \approx \sqrt{54.56} \approx 7.39\ \text{km} $
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