A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 4 ft, the length is 11 ft, and the top of the tank is 10 feet under the ground. The density of gasoline is 42 lb/ ft^3

Consider a slice of gasoline that is Δy ft thick and located y ft above the center of the cylinder. Write an expression giving the work required to pump the slice out

Question

A gas station stores its gasoline in a tank underground. The tank is a cylinder lying horizontally on its side. The radius is 4 ft, the length is 11 ft, and the top of the tank is 10 feet under the ground. The density of gasoline is 42 lb/ ft^3

Consider a slice of gasoline that is Δy ft thick and located y ft above the center of the cylinder. Write an expression giving the work required to pump the slice out

anonymous · Answer

$$
Work = Force \times Distance_{to\ the\ top}
$$We let for be equal to the gravitational force because that is the minimum force needed to suck the gasoline out.$$
Force = Mass \times Acceleration_{gravity}
$$Still need mass...$$
Mass = Volume \times Density
$$They gave us density, but we need volume.  Remember that we are trying to find the volume of a cylinder.$$
Volume = \pi \times Radius^2 \times Height 
$$Putting it all together, we get: $$
Work = \pi \times Radius^2\times Height\times Density\times Acceleration_{gravity} \times Distance_{to\ the\ top}
$$