Question

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

Answer 1

radius is 4.5 km

Explanation:

Given :

Total number of people living in the area = 1.15 million = 1150000

Population density = 18075 people per sq kilometer

To find:

Radius of region = ?

Solution:

Population density of a region is defined as the ratio of total population divided by the area of the region.

Area here is circular. Let the radius be = r

Area of circle is given as
`\pi r^2`

Formula:

`Population\ Density = (Total\ population)/(\pi r^2)`

Putting the values:

`18075 = (1150000)/(\pi r^2)\\\Rightarrow r^2 = (1150000)/(18075\pi )\\\Rightarrow r^2 = (63.62)/(\pi )\\\Rightarrow r^2 = 20.26\\\Rightarrow \bold{r=4.5\ km}`

Therefore, radius is 4.5 km.