To find the volume of a pyramid with a square base, we would follow these steps:
1. Determine the side length of the square base:
Since we know the perimeter of the base is 18.1 feet, and the base is square, we can divide the perimeter by 4 (because a square has four equal sides) to find the length of one side.
[tex]\[ \text{Side length} = \frac{\text{Perimeter of base}}{4} = \frac{18.1 \text{ ft}}{4} = 4.525 \text{ ft} \][/tex]
2. Calculate the area of the square base:
The area of a square is found by squaring the length of one side.
[tex]\[ \text{Base area} = (\text{Side length})^2 = (4.525 \text{ ft})^2 = 20.475625 \text{ ft}^2 \][/tex]
3. Compute the volume of the pyramid:
The volume of a pyramid is given by the formula: [tex]\(\frac{1}{3}\)[/tex] times the base area times the height of the pyramid.
[tex]\[ \text{Volume of pyramid} = \frac{1}{3} \times \text{Base area} \times \text{Height} \][/tex]
[tex]\[ \text{Volume of pyramid} = \frac{1}{3} \times 20.475625 \text{ ft}^2 \times 28.1 \text{ ft} \][/tex]
[tex]\[ \text{Volume of pyramid} = 191.7883541666667 \text{ ft}^3 \][/tex]
4. Round the answer to the nearest tenth:
Finally, we round the volume to the nearest tenth of a cubic foot for the final answer.
[tex]\[ \text{Rounded volume} = 191.8 \text{ ft}^3 \][/tex]
So, the volume of the pyramid, rounded to the nearest tenth, is [tex]\( 191.8 \text{ cubic feet} \)[/tex].
