Final answer:
To find the volume of the pyramid, first calculate the side length of the square base from the given perimeter, then calculate the base area, and finally apply the volume formula for a pyramid. The final volume, rounded to the nearest tenth, is approximately 36.4 cubic meters.
Step-by-step explanation:
To find the volume of a pyramid with a square base where the perimeter of the base is 14m, and the height of the pyramid is 8.8m, we first need to calculate the side length of the base. Using the perimeter formula for a square, which is P = 4a, we can determine that one side of the base (a) is 14m ÷ 4 = 3.5m.
Next, we calculate the area of the base, which is a² or (3.5m) ² = 12.25m². Now, we apply the formula for the volume of a pyramid, which is V = (1/3) × (Base Area) × (Height). Plugging in our values, we get V = (1/3) × (12.25m²) × (8.8m).
The resulting volume is approximately 36.4 cubic meters after rounding to the nearest tenth.