Question

What is the volume of the rectangular pyramid? Round answer to nearest hundredth in decimal form.

Width: 16 mi

Length: 16 mi

Height: 8 mi

Answer 1

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:

1. First, calculate \(256 \times 8\):

\[
256 \times 8 = 2048 \, \text{mi}^3
\]

2. 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**.