To find the volume of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times B \times h \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height of the pyramid.
In this case, the base of the pyramid is a square with a side length of 16 miles. Therefore, the area of the base \( B \) is calculated as follows:
\[ B = \text{side} \times \text{side} = 16 , \text{miles} \times 16 , \text{miles} = 256 , \text{mi}^2 \]
The height \( h \) of the pyramid is given as 8 miles.
Now substituting the values into the volume formula:
\[ V = \frac{1}{3} \times 256 , \text{mi}^2 \times 8 , \text{mi} \]
Calculating this:
\[ V = \frac{1}{3} \times 256 \times 8 \]
Calculating \( 256 \times 8 \):
\[ 256 \times 8 = 2048 \]
Now divide by 3:
\[ V = \frac{2048}{3} \approx 682.67 , \text{mi}^3 \]
Thus, the volume of the rectangular pyramid is approximately
\[ \boxed{682.67} , \text{mi}^3 \]