To approach this problem, we're going to follow two key steps.
Firstly, we determine the area of the circle where the signal can reach. We determine this using the formula for the area of a circle which is pi * radius^2. Pi is a constant (approximately 3.14159) and the radius, which has been provided as 80 miles. Hence, the area of signal coverage is approximately 20106.19 square miles.
The second step involves determining the number of cars that can pick up the signal. As per the given data, we know that there are about 5 cars for every square mile. To find out how many cars are in the entire signal area, we simply multiply the total area of signal coverage (which we calculated as 20106.19 square miles) by the number of cars per square mile (which is 5). Thus, we get approximately 100530.96 cars.
Therefore, about 100531 cars will be able to pick up the signal from the radio station.