Question

the coverage area for a certain radio station can be modeled as a circle with the center at the stations transmitter and a radius of 25 miles. population density for the coverage area is 14.2 residents per square mile. to the nearest hundred, how many people reside within the statio coverage area?
a 111,500
b 27,900
c 2,200
d 1,100

Explanation:

Step1: Calculate the area of the circular coverage

The formula for the area of a circle is \(A=\pi r^{2}\). Given \(r = 25\) miles, we have \(A=\pi\times(25)^{2}=625\pi\) square miles. Using \(\pi\approx3.14\), then \(A\approx625\times3.14 = 1962.5\) square miles.

Step2: Calculate the number of residents

The population density \(d = 14.2\) residents per square mile. The number of residents \(N=d\times A\). Substitute \(d = 14.2\) and \(A\approx1962.5\) into the formula: \(N=14.2\times1962.5\).

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Rounding \(27867.5\) to the nearest hundred gives \(27900\).

Answer:

B. 27,900