About 1.15 million people live in a circular region with a population density of about 18,075 people per square kilometer. Find the radius of the region. Round your answer to the nearest tenth.
Question
About 1.15 million people live in a circular region with a population density of about 18,075 people per square kilometer. Find the radius of the region. Round your answer to the nearest tenth.
Solution
Sure, here's how you can solve this problem:
Step 1: Understand the problem The problem gives us the total population of the region (1.15 million people) and the population density (18,075 people per square kilometer). We are asked to find the radius of the region.
Step 2: Use the formula for population density Population density is defined as the number of people per unit area. So, we can write the formula as:
Population Density = Total Population / Area
Step 3: Rearrange the formula to solve for Area We can rearrange the formula to solve for Area:
Area = Total Population / Population Density
Step 4: Substitute the given values into the formula Substitute the given values into the formula:
Area = 1.15 million people / 18,075 people per square kilometer Area ≈ 63.6 square kilometers
Step 5: Use the formula for the area of a circle The area of a circle is given by the formula:
Area = πr²
where r is the radius of the circle.
Step 6: Rearrange the formula to solve for r We can rearrange the formula to solve for r:
r = sqrt(Area / π)
Step 7: Substitute the value of Area into the formula Substitute the value of Area into the formula:
r = sqrt(63.6 km² / π) r ≈ 4.5 km
So, the radius of the region is approximately 4.5 kilometers.
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