Final answer:
To calculate the volume of a pyramid with a square base, divide the perimeter by 4 to get the side length, square it to find the base area, and then use the formula (1/3) × base area × height. The volume is 145.2 cm³ when rounded to the nearest tenth. When rounded to the nearest tenth, the volume of the pyramid is 145.2 cm³.
Step-by-step explanation:
To find the volume of a pyramid with a square base, when given the perimeter of the base and the height of the pyramid, you can follow these steps:
- First, calculate the side length of the base by dividing the perimeter by 4 (since there are four sides to a square).
- Next, calculate the area of the base by squaring the side length found in step 1.
- Lastly, use the volume formula for a pyramid, which is V = (1/3) × base area × height, to find the volume.
Given: Perimeter of base = 18.4 cm, Height of pyramid = 20.6 cm
Side length of base (s) = Perimeter / 4 = 18.4 cm / 4 = 4.6 cm
Base area (A) = s² = (4.6 cm)² = 21.16 cm²
Volume of pyramid (V) = (1/3) × A × height = (1/3) × 21.16 cm² × 20.6 cm = 145.1976 cm³
When rounded to the nearest tenth, the volume of the pyramid is 145.2 cm³.