Short answer: Density = 79.6 bacteria / in^2
Step One
Find the area of the petri dish
d = 4 inches
r = d/2
r = 4/2 = 2 inches.
pi = 3.14
Area = pi * r^2
Area = 3.14 * 2 * 2
Area = 12.56
Step Two
Find the density of the population.
Density = total population / Area
total population = 1000
Area = 12.56
Sub and Solve
Density = 1000 / 12.56
Density = 79.6 bacteria per square inch.