# A Waste Treatment Pond Is 50m Long

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 $1{0}^{4}10^4$ kilograms.

Share

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:

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

2. Convert Density to kg/m³:

The given density of the waste is $85.3 {3}^{}85.3 \, \text\left\{lbm/ft\right\}^3$85.3. 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.

3. Calculate the Mass of the Pond Contents:

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

4. Convert Mass to $1{0}^{4}10^4$104 kg:

The weight of the pond contents is approximately $205.18×1{0}^{4}205.18 \times 10^4$205.18×104 kilograms.