Respuesta :
Answer:
The number of people live in circular region are 319,990
Step-by-step explanation:
A circular region with a 4-mile radius has a population density of about 6366 people per square mile.
[tex[\text{Population density }=6366\text{ people/mi}^2[/tex]
Area of circular region = πr²
where, radius (r) = 4 miles
Area of circular region = π x 4²
= 16π mi²
We need to find number of people who live in the circular region .
Number of people = Population density x Area of region
Number of people = 6366 x 16π
= 319,990
Hence, The number of people live in circular region are 319,990
The number of people who live in the region is 319,990 people
From the question,
The radius of the circular region is 4-mile and
Population density is about 6366 people per square mile
To determine the number of people who live in the region,
From the formula for population density
[tex]Population \ density = \frac{Number \ of \ people }{Land \ area}[/tex]
∴ [tex]Number \ of \ people = Population \ density \times Land \ area[/tex]
Therefore, we will first determine the land area of the circular region.
Since, the region is circular, we can determine the area of the region using the formula for finding area of a circle.
Area of a circle is given by the formula
[tex]A = \pi r^{2}[/tex]
Where [tex]A[/tex] is the area
and [tex]r[/tex] is the radius
From the question
[tex]r = 4 \ mile[/tex]
∴ Area of the region = [tex]\pi \times 4^{2}[/tex]
Area of the region = [tex]\pi \times 16[/tex]
Take [tex]\pi = 3.14159[/tex]
∴ Area of the region = [tex]3.14159 \times 16[/tex]
Area of the region = [tex]50.26544 \ square \ mile[/tex]
Now, for the number of people who live in the region,
Put the values into the equation
[tex]Number \ of \ people = Population \ density \times Land \ area[/tex]
From the question, population density = 6366 people per square mile
From above, area of the region = 50.26544 square mile
[tex]Number \ of \ people = 6366 \times 50.26544[/tex]
[tex]Number \ of \ people = 319989.79104[/tex]
∴ Number of people ≅ 319990 people
Hence, the number of people who live in the region is 319,990 people.
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