Question

A circular region has a population of about 260000 people and a population density of about 135 people per square mine . find the radius of the region

Answer 1

Answer:

24.76 mine

Step-by-step explanation:

The first thing is to calculate the area of the region, which we can calculate since we have the density and the population. The area would be the quotient between population and density:

260000/135 = 1925.93

The area would be 1925.93 square mine

We know that the area is given by:

A = pi * r ^ 2

we solve to r

r ^ 2 = A / pi

r ^ 2 = 1925.92 / 3.14

r ^ 2 = 613.3

r = 24.76

the radius is equal to 24.76 mine

Answer 2

Answer:

$\rho = \frac{People}{Area}$

$A= \frac{People}{\rho}$

$A = \frac{260000 people}{135 \frac{people}{mine^2}}= 1925.926 mine^2$

$A = \pi r^2$

$r= \sqrt{\frac{A}{\pi}}= \sqrt{\frac{1925.926 mine^2}{\pi}}=24.760 mine$

Step-by-step explanation:

For this case we need to use the definition of population density:

$\rho = \frac{People}{Area}$

For this case the population is P =260000 people. And the population density is $\rho = 135 \frac{people}{mine^2}$

If we solve for the area we got:

$A= \frac{People}{\rho}$

And replacing we got:

$A = \frac{260000 people}{135 \frac{people}{mine^2}}= 1925.926 mine^2$

Since we are assuming a circular pattern the area is given by:

$A = \pi r^2$

And solving for r we got:

$r= \sqrt{\frac{A}{\pi}}= \sqrt{\frac{1925.926 mine^2}{\pi}}=24.760 mine$