Answer:
The radius of the region is 12 miles
Step-by-step explanation:
step 1
Find the area of the circular region
we know that
About 52000 people live in a circular region with a population density of about 115 people per square mile
using proportion
Let
x ------> the area of the circular region
[tex]\frac{115}{1}\frac{people}{mi^{2}}=\frac{52,000}{x}\frac{people}{mi^{2}} \\ \\ x=52,000/115\\ \\x=452.17\ mi^2[/tex]
step 2
Find the radius of the circular region
we know that
The area of the circular region is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=452.17\ mi^2[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]452.17=(3.14)r^{2}[/tex]
[tex]r^{2}=452.17/(3.14)[/tex]
[tex]r^{2}=144[/tex]
[tex]r=12\ mi[/tex]
