Final answer:
The volume of the pyramid is 120.4 cubic feet.
Step-by-step explanation:
To find the volume of a pyramid, we use the formula V = 1/3 * base area * height. In this case, the base of the pyramid is a square with a perimeter of 18.5 ft, which means each side has a length of 18.5/4 = 4.625 ft. The area of a square is calculated by multiplying the length of one side by itself, so the base area of the pyramid is 4.625 * 4.625 = 21.390625 ft^2. The height of the pyramid is given as 7.6 ft.
To find the volume, we plug in the values into the formula: V = 1/3 * 21.390625 * 7.6 = 120.4 ft^3. We round this answer to the nearest tenth, which gives us a final volume of 120.4 cubic feet.
Explanation: The first step in finding the volume of a pyramid is to determine the base area. In this case, we are given the perimeter of the base, which is 18.5 ft. We know that the perimeter of a square is equal to 4 times the length of one side, so we divide 18.5 by 4 to find the length of one side, which is 4.625 ft. Since the base of the pyramid is a square, all sides are equal and have a length of 4.625 ft.
Next, we use the formula for the area of a square, which is length * width. In this case, the length and width are both 4.625 ft, so we multiply 4.625 by itself to get the base area of 21.390625 ft^2.
Now, we have all the necessary values to plug into the formula for finding the volume of a pyramid. The height of the pyramid is given as 7.6 ft, so we substitute this value along with the base area into the formula V = 1/3 * base area * height. After simplifying, we get V = 1/3 * 21.390625 * 7.6 = 120.4 ft^3.
To round our final answer to the nearest tenth, we look at the digit in the hundredths place, which is 4. Since it is less than 5, we keep the digit in the tenths place as it is. Therefore, the final volume of the pyramid is 120.4 cubic feet.