Question

Find the volume of a pyramid with a square base, where the side length of the base is

18.7 ft and the height of the pyramid is 8.8 ft.

Answer 1

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.

`\[ B = (18.7 \, \text{ft})^2 = 349.69 \, \text{ft}^2 \]`

Now, substitute the values into the volume formula:

`\[ V = (1/3) * 349.69 \, \text{ft}^2 * 8.8 \, \text{ft} \]`

`\[ V = 2,118.72 \, \text{ft}^3 \]`

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.

Answer 2

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.