There are approximately 106 ants per square foot of the colony.
Step-by-step explanation:
Step 1:
The colony where the ants live is in the form of a circle with a radius of 3 feet.
The area of a circle is given by multiplying π with the square of the radius (r²). Here the radius r is 3 feet.
The area of a circle [tex]=\pi r^{2}.[/tex]
The area of the given circle [tex]= \pi (3^{2}) = 3.1415(9) = 28.2735[/tex] square feet.
Step 2:
To find the population density of the ants per square foot, we divide the number of ants in the entire area by the area of their colony.
The population density [tex]\frac{3,000}{28.2735} = 106.1064.[/tex]
Rounding this off, we get 106. So there are approximately 106 ants per square foot of the colony.
