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

Question

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 14 ft, and the top of the tank is 10 feet under the ground Assume the tank is full and a of the gasoline will be pumped to the surface of the ground. The density of gasoline is 42 lb/ ft3 (a) Consider a slice of gasoline that is Ay ft thick and located y ft above the center of the cylinde r. U see Delta or the d for A. Leave m in your answer. ft3 Volume of slice Displacement of slice (b) Find the endpoints of the integral needed to find the exact work required to pump all the gasoline to the surface of the ground. Lower endpoint upper endpoint

Explanation / Answer

(b)

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 * 14
V = 126*pi ft^3
The weight of the gasonline is:
Wt = 42 * 126*pi = 5292*pi lb
Work is Force times Displacement:
W = 5292*pi * 13 = 68796*pi lb-ft

displacement is 13 (from r=3 to r=16)

therefore

lower endpoints=3 (from middle of the cylinder)

upper endpoints=16 (upto to level of the surface 10+3+3=16)

(a)

sorry, does not able to solve (actually not able to understand the problem)

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