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A Waste Treatment Pond Is 50m Long

Updated July 7, 2024

A waste treatment pond is 50 meters long, 15 meters wide, and has an average depth of 2 meters. The density of the waste is 85.3 lbm/ft³. Calculate the weight of the pond contents in 10410^4 kilograms.

1 Answer

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AnonymousJuly 7, 2024
  1. Calculate the Volume of the Pond:

    The dimensions of the pond are:

    • Length: 50 m
    • Width: 15 m
    • Depth: 2 m

    The volume VV of the pond is:

    V=length×width×depthV = \text{length} \times \text{width} \times \text{depth}
    V=50 m×15 m×2 mV = 50 \, \text{m} \times 15 \, \text{m} \times 2 \, \text{m}
    V=1500 m3V = 1500 \, \text{m}^3

  2. Convert Density to kg/m³:

    The given density of the waste is 85.3 lbm/ft385.3 \, \text{lbm/ft}^385.3. We need to convert this to kg/m³.

    • 1 pound mass (lbm) is approximately 0.45359237 kilograms.
    • 1 cubic foot (ft³) is approximately 0.0283168 cubic meters.

    Density in kg/m3=85.3 lbm/ft3×0.45359237 kg/lbm÷0.0283168 m3/ft3\text{Density in kg/m}^3 = 85.3 \, \text{lbm/ft}^3 \times 0.45359237 \, \text{kg/lbm} \div 0.0283168 \, \text{m}^3/\text{ft}^3
    Density in kg/m3=85.3×0.45359237÷0.0283168\text{Density in kg/m}^3 = 85.3 \times 0.45359237 \div 0.0283168
    Density in kg/m3≈1367.89 kg/m3\text{Density in kg/m}^3 \approx 1367.89 \, \text{kg/m}^3

  3. Calculate the Mass of the Pond Contents:

    Mass=Volume×Density\text{Mass} = \text{Volume} \times \text{Density}
    Mass=1500 m3×1367.89 kg/m3\text{Mass} = 1500 \, \text{m}^3 \times 1367.89 \, \text{kg/m}^3
    Mass≈2051835 kg\text{Mass} \approx 2051835 \, \text{kg}

  4. Convert Mass to 10410^4104 kg:

    Mass in 104 kg=2051835 kg104\text{Mass in } 10^4 \, \text{kg} = \frac{2051835 \, \text{kg}}{10^4}​ Mass in 104 kg≈205.18\text{Mass in } 10^4 \, \text{kg} \approx 205.18

Answer:

The weight of the pond contents is approximately 205.18×104205.18 \times 10^4205.18×104 kilograms.