To find the volume of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a square pyramid, the base area is given by the side length squared. Since the pyramid has a side length of 16 miles, we can calculate the base area as follows:
\[ \text{Base Area} = \text{side length}^2 = 16 , \text{miles} \times 16 , \text{miles} = 256 , \text{miles}^2 \]
The height of the pyramid is given as 8 miles. Now we can substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 256 , \text{miles}^2 \times 8 , \text{miles} \]
Calculating this:
\[ V = \frac{1}{3} \times 2048 , \text{miles}^3 = \frac{2048}{3} , \text{miles}^3 \approx 682.67 , \text{miles}^3 \]
Rounding to the nearest hundredth, the volume of the rectangular pyramid is:
\[ \boxed{682.67} , \text{mi}^3 \]