Question

About $650,000$ people live in a circular region with a $6$-mile radius.

Find the population density in people per square mile.

Answer 1

Step-1: Calculate the area of the circular region:

Given that the radius of the circular region $r$ (say) is $6$ mile.

Area of the circular region $A={\mathrm{\pi r}}^2$sq. units.

$\begin{array}{rcl}A& =& \mathrm{\pi }{\left(6\right)}^2\\ & \Rightarrow & A=\mathrm{\pi }\times 36\\ & \Rightarrow & A=3.14\times 36\\ \therefore A& =& 113.04{\mathrm{mile}}^2\end{array}$

Step-2: Calculate the population density

Given that the population of the circular region is $650,000$

The formula for the population density of the region is $\frac{\mathrm{Population}}{\mathrm{Area}}$

Substitute $650,000$ for population and area as $113.04{\mathrm{mile}}^2$

So $\begin{array}{rcl}\text{Population density}& =& \frac{650000}{113.04}\\ \therefore \text{Population density}& =& 5750.2\mathrm{people}\mathrm{per}\mathrm{square}\mathrm{mile}\end{array}$

Hence, population density is $5750.2$ people per square mile.