To calculate the area reached by the radio waves, we first need to determine the radius of the circle of broadcast range. The radius is half of the diameter.
Given that the diameter is 96 miles, we find the radius as follows:
\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{96 \text{ mi}}{2} = 48 \text{ mi} \]
Next, we use the formula for the area \( A \) of a circle, which is given by:
\[ A = \pi r^2 \]
Using \( \pi \approx 3.14 \) and substituting the radius we found:
\[ A = 3.14 \times (48 \text{ mi})^2 \] \[ A = 3.14 \times 2304 \text{ mi}^2 \] \[ A \approx 7238.56 \text{ mi}^2 \]
Thus, the area reached by the radio waves is approximately \( 7238.56 \) square miles.