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

Guest Sep 15, 2017

#1**+1 **

**density area people**

**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**

Let **A** = area of the circular region

Let **r **= radius of the circular region

\(\mathbf{A = \ ?}\)

\(\begin{array}{|rcll|} \hline A &=& 1500000\ \text{people} \times \frac{1\ km^2}{18075\ \text{people} } \\ &=& \frac{1500000}{18075} \ km^2 \\ &=& 82.9875518672 \ km^2 \\ \hline \end{array}\)

\(\mathbf{r = \ ?}\)

\(\begin{array}{|rcll|} \hline \pi \ r^2 &=& A \\ r^2 &=& \frac{A}{\pi} \\ r &=& \sqrt{ \frac{A}{\pi} } \\ &=& \sqrt{ \frac{82.9875518672}{\pi} } \\ &=& \sqrt{ 26.4157581895 } \\ \mathbf{r} &\mathbf{=}& \mathbf{ 5.13962626944 \ km } \\ \hline \end{array}\)

The radius of the region is \(\mathbf{\approx5.14\ km}\)

heureka
Sep 15, 2017