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 5 ft, the length is 14 ft, and the top of the tank is 10 feet under the ground. Assume the tank is full and all of the gasoline will be pumped to the surface of the ground. The density of gasoline is 42 lb/ ft^3. Consider a slice of gasoline that is Ay ft thick and located y ft above the center of the cylinder. Use Delta or the CalcPad for Delta . Leave n in your answer. Volume of slice : = 14(squareroot5-y^2)^2 Delta y ft^3 Displacement of slice : = (12-y) ft^2 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 = 5 Upper endpoint = 14

Explanation / Answer

The slice would be in the shape of a rectangle with thickness y ft

The length of the slice would be the length of the cylinder , 14ft

By Pythagoras Theorem , the bredth can be calculated , 2 . ( ( 52 - y2) ) ft

=> Volume of the slice = Length * Bredth * Thickness

=> V = 14 * 2 . ( ( 52 - y2) ) * y

The displacement of the slice is calculated with reference to the center and to the top

=> Final Position with repect to center = 15 ft

=> Initial Position with respect to center = y ft

=> Displacement = Final - Initial = ( 15 - y ) ft

The range of y goes from top of tank which is 5 ft above the center to the bottom of the tank which is 5 ft below the center. Above center is taken as positive values and below center is taken as negative values.

=> -5 < y < 5

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