help A gas station stores its gasoline in a tank underground. The tank is a cyli

Question

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A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 3 ft, the length is 16 ft, and the top of the tank is 10 feet under the ground. The density of gasoline is 42 lb/ ft3. Consider a slice of gasoline that is delta y ft thick and located y ft above the center of the cylinder. Use Delta or the CalcPad for delta if necessary. Volume of slice = ft3 Displacement of slice = ft Find the exact work required to pump all the gasoline out. Give your answer in terms of pi . ft-lb

Explanation / Answer

If the tank is full:
The average depth of the gasonline is 10 + 3 = 13 feet underground.
The volume of the tank is:
V = pi * r^2 * h
V = pi * 3^2 * 16
V = 144*pi ft^3

The weight of the gasonline is:

W = 42 * 144*pi = 6048*pi lb

Work is Force times Displacement:
W = 6048*pi * 16 = 96768*pi =~ 304006.34 lb-ft
That's how much work is needed to pump the gasonline up to ground level.

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