To find the volume of a square pyramid, you can use the formula:
\[ V = \frac{1}{3} \times B \times h \]
where \(B\) 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.
- The area \(B\) of the base can be calculated as:
\[ B = \text{side} \times \text{side} = 16 , \text{mi} \times 16 , \text{mi} = 256 , \text{mi}^2 \]
- The height \(h\) of the pyramid is given as 8 miles.
Now, plug these values into the volume formula:
\[ V = \frac{1}{3} \times 256 , \text{mi}^2 \times 8 , \text{mi} \]
Calculating this:
\[ V = \frac{1}{3} \times 2048 , \text{mi}^3 = \frac{2048}{3} , \text{mi}^3 \approx 682.6667 , \text{mi}^3 \]
Rounding this to the nearest hundredth:
\[ V \approx 682.67 , \text{mi}^3 \]
Thus, the volume of the rectangular pyramid is approximately:
\[ \boxed{682.67 , \text{mi}^3} \]