Final answer:
The volume of the pyramid is calculated by first finding the side length of the square base from the given perimeter, then using the side length to determine the base area, and finally applying the volume formula for pyramids. The calculated volume is 12.5 cm³.
Step-by-step explanation:
To find the volume of a pyramid with a square base, you first need to determine the length of a side of the base. Since the perimeter of the base is 8.6 cm, and a square has four equal sides, each side is 8.6 cm divided by 4, which is 2.15 cm. The formula for finding the volume of a pyramid is V = (1/3) × base area × height.
To calculate the base area, square the side length: 2.15 cm × 2.15 cm = 4.6225 cm². Then, apply the volume formula by multiplying the base area by the height and dividing by 3: V = (1/3) × 4.6225 cm² × 8.1 cm = 12.519075 cm³. Round this to the nearest tenth to get 12.5 cm³ as the pyramid's volume.