To find the volume of a rectangular pyramid, you can use the formula:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
The base of the pyramid is a rectangle, so we first calculate the area of the base:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 7.5 , \text{mi} \times 7 , \text{mi} = 52.5 , \text{mi}^2 \]
Now, using the height of the pyramid (5 mi), we can calculate the volume:
\[ \text{Volume} = \frac{1}{3} \times 52.5 , \text{mi}^2 \times 5 , \text{mi} \]
Calculating the volume:
\[ \text{Volume} = \frac{1}{3} \times 52.5 \times 5 = \frac{262.5}{3} = 87.5 , \text{mi}^3 \]
Thus, the volume of the rectangular pyramid is \( 87.5 , \text{mi}^3 \).