density area people

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 made a simple mistake in copying:

1.15 million / 18,075 =63.6238 Sq. Km- The area of the city region.

63.6238 = Pi x r^2

r^2 = 63.6238 / Pi

r^2 =20.252   take the sqrt of both sides

r = ~4.50 Km radius of the region