How many gallons of water are contained in a 12" water main that is 500 ft long?

To determine how many gallons of water are in a 12-inch water main that is 500 feet long, you need to calculate the volume of the cylinder formed by the water main. The formula for the volume of a cylinder is:

[ V = \pi r^2 h ]

Where ( V ) is volume, ( r ) is the radius, and ( h ) is the height (or length in the case of a horizontal section).

1. Convert the diameter of the water main (12 inches) to feet to match the length measurement. Since there are 12 inches in a foot, the diameter in feet is 1 foot. The radius is half of the diameter, which is 0.5 feet.

2. The height of the cylinder corresponds to the length of the water main, which is 500 feet.

Substituting the dimensions into the volume formula gives:

[ V = \pi (0.5)^2 (500) ]

Calculating ( (0.5)^2 ):

[ (0.5)^2 = 0.25 ]

Now substituting back into the volume formula:

[ V = \pi (0.25) (500) ]

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