Question

The density of water is 1.00 g/mL. If your swimming pool holds 208,000 gallons of water, what are the conversion factors that are needed to find the weight of the water in a filled swimming pool in tons?A) 1 ton - 2000 pounds3.7854 gal - 1L1000 L - 1 mL1 pound - 453.59 gB) 1 ton - 2000 pounds3.7854 gal -1 L1000 mL - 1 L1 pound - 453.59 gC) 1 ton - 2000 pounds3.7854 L - 1 gal1000 L - 1 mL1 pound-453.59 gD) 1 ton - 2000 pounds3.7854L - 1 gal1000 mL - 1 L1 pound - 453.59 g

Answer 1

1) List the known and unknown quantities.

Volume: 208,000 gallons.

Density: 1.00 g/mL.

2) Convert gallons to liters.

3.7854 L = 1 gal.

`L=208000\text{ }gal*\frac{3.7854\text{ }L}{1\text{ }gal}=787365.651\text{ }L`

3) Convert g/mL to pound/L

1 pound = 453.59 g

1000 mL = 1 L

`(kg)/(L)=1.00(g)/(mL)*\frac{1000\text{ }mL}{1\text{ }L}*\frac{1\text{ }pound}{453.59\text{ }g}=2.205(pound)/(L)`

4) Mass of water in kg.

`density=(mass)/(volume)`
`mass=density*volume`
`mass=2.205(pound)/(L)*787365.651\text{ }L=1736141.26\text{ }pounds`

5) Convert pounds to tons.

1 ton = 2000 pounds

`ton=1736141.26\text{ }pounds*\frac{1\text{ }ton}{2000\text{ }pounds}=868.07\text{ }tons`

The conversion factors needed are those in option D.

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