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Find the volume of a pyramid with a square base, where the perimeter of the base is 14.3cm and the height of the pyramid is 21.2cm. Round your answer to the nearest tenth of a cubic centimeter. Answer: cm^(3)

Find the volume of a pyramid with a square base, where the perimeter of the base is 14.3 cm 14.3 \mathrm{~cm} and the height of the pyramid is 21.2 cm 21.2 \mathrm{~cm} . Round your answer to the nearest tenth of a cubic centimeter.\newlineAnswer: cm3 \mathrm{cm}^{3}

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Q. Find the volume of a pyramid with a square base, where the perimeter of the base is 14.3 cm 14.3 \mathrm{~cm} and the height of the pyramid is 21.2 cm 21.2 \mathrm{~cm} . Round your answer to the nearest tenth of a cubic centimeter.\newlineAnswer: cm3 \mathrm{cm}^{3}
  1. Find Side Length: First, we need to find the length of one side of the square base. Since the perimeter of a square is the sum of all its sides, we divide the perimeter by 44. \newlinePerimeter of the square base = 14.3 cm14.3\,\text{cm} \newlineLength of one side of the square base = Perimeter ÷4\div 4 \newlineLength of one side = 14.3 cm÷414.3\,\text{cm} \div 4
  2. Calculate Side Length: Now, let's calculate the length of one side of the square base.\newlineLength of one side = 14.3 cm÷414.3\,\text{cm} \div 4\newlineLength of one side = 3.575 cm3.575\,\text{cm}
  3. Calculate Base Area: Next, we calculate the area of the square base using the length of one side.\newlineArea of the square base = (Length of one side)\newlineArea of the square base = (3.575 cm)2(3.575 \, \text{cm})^2
  4. Use Volume Formula: Let's perform the calculation for the area of the square base.\newlineArea of the square base = (3.575 cm)2(3.575 \, \text{cm})^2\newlineArea of the square base = 12.781625 cm212.781625 \, \text{cm}^2
  5. Calculate Volume: Now, we will use the formula for the volume of a pyramid, which is (13)×(base area)×(height)(\frac{1}{3}) \times (\text{base area}) \times (\text{height}).
    Volume of the pyramid = (13)×(base area)×(height)(\frac{1}{3}) \times (\text{base area}) \times (\text{height})
    Volume of the pyramid = (13)×(12.781625 cm2)×(21.2 cm)(\frac{1}{3}) \times (12.781625 \, \text{cm}^2) \times (21.2 \, \text{cm})
  6. Round to Nearest Tenth: Finally, we calculate the volume of the pyramid.\newlineVolume of the pyramid = (13)×(12.781625 cm2)×(21.2 cm)(\frac{1}{3}) \times (12.781625 \text{ cm}^2) \times (21.2 \text{ cm})\newlineVolume of the pyramid = 90.28875 cm390.28875 \text{ cm}^3
  7. Round to Nearest Tenth: Finally, we calculate the volume of the pyramid.\newlineVolume of the pyramid = (13)×(12.781625 cm2)×(21.2 cm)(\frac{1}{3}) \times (12.781625 \text{ cm}^2) \times (21.2 \text{ cm})\newlineVolume of the pyramid = 90.28875 cm390.28875 \text{ cm}^3We need to round the answer to the nearest tenth of a cubic centimeter.\newlineRounded volume of the pyramid = 90.3 cm390.3 \text{ cm}^3

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