Geometry

A biologist is researching the population density of lizards near a boulder in a desert. The biologist counts 15 lizards within a radius of 14 mi of the boulder.

What is the population density of lizards?

 Use 3.14 for pi and round only your final answer to the nearest whole number.

$The \ population \ density \ of \ lizards \ is$

$= \frac{15\ lizards }{2\times 3.14 \times {14}^2 square\ miles} = ( \frac{15}{1230.88}=0.012)\frac{ lizards }{square\ mile}$

$\approx 1 \frac {1 lizard }{square \ mile}$

  !

sine

$= \frac{15\ lizards }{ 3.14 \times {14}^2 square\ miles} = ( \frac{15}{615.44}=0.0244)\frac{ lizards }{square\ mile}$

$\approx 1 \frac {1 lizard }{square \ mile}$

  asinus

This isn’t a sustainable population. It’s probably 1/4 mile radius.

15/(3.14*.25²) = 76.43

76 lizards per square mile.

Note that Density = $\frac{\text{population}}{\text{area}}$

As stated in the question, there are 15 lizards, and the area of the circle that surrounds the boulder is simply $14^2\times\pi$or $196\pi$Thus the answer is $\frac{15}{196\pi} \approx \frac{1}{41.0293333}$