To find the volume of a rectangular pyramid, the formula is:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, we calculate the base area. The base area of a rectangular pyramid is given by:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
Substituting the given dimensions:
\[ \text{Base Area} = 16 , \text{mi} \times 16 , \text{mi} = 256 , \text{mi}^2 \]
Next, we use the height of the pyramid, which is given as 8 mi. Now we can substitute the base area and height into the volume formula:
\[ \text{Volume} = \frac{1}{3} \times 256 , \text{mi}^2 \times 8 , \text{mi} \]
Calculating this:
- First, calculate \(256 \times 8\):
\[ 256 \times 8 = 2048 , \text{mi}^3 \]
- Now, divide by 3:
\[ \text{Volume} = \frac{2048}{3} \approx 682.6667 , \text{mi}^3 \]
Rounding this to the nearest hundredth:
\[ \text{Volume} \approx 682.67 , \text{mi}^3 \]
Thus, the volume of the rectangular pyramid is approximately 682.67 mi³.