To find the area of a circle, we use the formula:
\[ \text{Area} = \pi r^2 \]
First, we need to find the radius. The radius \( r \) is half of the diameter. Given that the diameter is 21 mi, the radius is:
\[ r = \frac{21}{2} = 10.5 \text{ mi} \]
Now, we can substitute \( r \) into the area formula. Using \( \pi \approx 3.14 \):
\[ \text{Area} = 3.14 \times (10.5)^2 \]
Calculating \( (10.5)^2 \):
\[ (10.5)^2 = 110.25 \]
Now, substitute back into the area formula:
\[ \text{Area} = 3.14 \times 110.25 \]
Calculating the area:
\[ \text{Area} \approx 346.19 \text{ mi}^2 \]
Rounding to the nearest hundredths place, the area is:
\[ 346.19 \text{ mi}^2 \]
Thus, the correct response is:
346.19 mi²