Final Answer:
The volume of the pyramid is 2,118.72 cubic feet.
Step-by-step explanation:
To find the volume of a pyramid, you use the formula V = (1/3) * B * h, where B is the area of the base and h is the height. In this case, the pyramid has a square base, so the area of the base (B) is calculated by squaring the side length of the base.
![\[ B = (18.7 \, \text{ft})^2 = 349.69 \, \text{ft}^2 \]](https://img.qammunity.org/2023/formulas/mathematics/high-school/ugeu3quno423y88rrqulmdytpwrxgvykp8.png)
Now, substitute the values into the volume formula:
![\[ V = (1/3) * 349.69 \, \text{ft}^2 * 8.8 \, \text{ft} \]](https://img.qammunity.org/2023/formulas/mathematics/high-school/q2uot1zwj19eauz2gberph77rg7y4p5m6g.png)
![\[ V = 2,118.72 \, \text{ft}^3 \]](https://img.qammunity.org/2023/formulas/mathematics/high-school/fe0kv0so74cclyacdjpijhegl85sg5mmin.png)
So, the final answer is 2,118.72 cubic feet. This result represents the amount of space enclosed by the pyramid. The (1/3) factor in the formula accounts for the pyramid's geometric relationship to a prism with the same base and height. Essentially, you are finding the volume of a cube with side length 18.7 feet and then taking one-third of that volume since the pyramid is a three-dimensional shape with a triangular cross-section.