Question

prymid base of 16 mi center line 8 mi

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

Answer 1

To find the volume of a rectangular pyramid, you can use the formula:

\[
V = \frac{1}{3} \times B \times h
\]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height of the pyramid.

Given:
- The base of the pyramid is a square with a side length of 16 miles. Therefore, the area \( B \) of the base is:

\[
B = \text{side} \times \text{side} = 16 \, \text{mi} \times 16 \, \text{mi} = 256 \, \text{mi}^2
\]

- 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 the volume:

\[
V = \frac{1}{3} \times 2048 \, \text{mi}^3
\]

\[
V = \frac{2048}{3} \approx 682.67 \, \text{mi}^3
\]

So, the volume of the rectangular pyramid is approximately \( \boxed{682.67 \, \text{mi}^3} \).