Use the image to answer the question.

Question

An illustration shows a square rectangular pyramid with a side length of 16 miles and a perpendicular height of 8 miles. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.

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

mi.3

Answer 1

The volume \( V \) of a rectangular pyramid is calculated using the formula:

\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

For a square pyramid, the base area \( A \) can be calculated as:

\[ A = \text{side length}^2 \]

In this case, the side length is 16 miles, so:

\[ A = 16^2 = 256 \text{ square miles} \]

The height \( h \) of the pyramid is given as 8 miles. Now we plug the base area and height into the volume formula:

\[ V = \frac{1}{3} \times 256 \times 8 \]

Calculating this step-by-step:

1. Multiply the base area by the height:

   \[ 256 \times 8 = 2048 \]

2. Now calculate the volume:

   \[ V = \frac{1}{3} \times 2048 = \frac{2048}{3} \approx 682.6667 \]

Rounding to the nearest hundredth, the volume of the pyramid is:

\[ \boxed{682.67} \text{ mi}^3 \]