Final answer:
The volume of wastewater in 100 feet of 10-inch force main is approximately 408 gallons, which is option (c). This calculation is based on the volume formula for a cylinder and converting cubic feet to gallons.
Step-by-step explanation:
To find the volume of wastewater contained in 100 feet of 10-inch force main, we start by converting the dimensions into consistent units and then apply the formula for the volume of a cylinder (V = πr2h), where r is the radius of the cylinder and h is the height or length of the cylinder.
First, we convert the diameter into a radius in feet: 10 inches / 2 = 5 inches, which is 5/12 feet (since there are 12 inches in a foot). Therefore, the radius is approximately 0.4167 feet. Now, we have the length of the pipe in feet which is 100 feet.
Next, we calculate the volume in cubic feet using the formula: V = π(0.4167 feet)2(100 feet) ≈ 54.62 cubic feet (using π ≈ 3.1416).
To convert cubic feet to gallons, we use the conversion factor 1 cubic foot = 7.48052 gallons. Therefore, the volume in gallons is 54.62 cubic feet × 7.48052 gallons/cubic foot ≈ 408.57 gallons.
Thus, the closest answer to the options given is (c) 408 gallons.