Answer:
The person can live at a distance of 113 miles
Explanation:
In this question, we are concerned with calculating how far a person live from a radio station and hear its broadcast given that the broadcast covers an area of 40,000 square miles.
Now this question is asking us to calculate the farthest distance from the radio station to the house of the person.
With the radio station being the center, what we are asked to calculate is the radius which is the distance from the center to the edge ( circumference)
Mathematically, the area can be calculated as
A = π * r^2
Here, we have the Area as 40,000 square miles
Thus,
40,000 = π * r^2
r^2 = 40,000/π
r = √(40,000/π)
r = 112.8379
As a whole number r = 113 miles