A tank containing oil is in the shape of a downward-pointing cone with its verti

Question

A tank containing oil is in the shape of a downward-pointing cone with its vertical axis perpendicular to ground level. (See a graph of the tank here.) In this exercise we will assume that the height of the tank is h-10 feet, the circular top of the tank has radius r = 5 feet, and that the oil inside the tank weighs 55 pounds per cubic foot How much work (W) does it take to pump oil from the tank to an outlet that is 5 feet above the top of the tank if, prior to pumping, there is only a half-tank of oil? Note: "half-tank" means half the volume in the tank. ft-lb

Explanation / Answer

Solution:

Volume V = (y/3)2 * y

W = (y/3)2 * y * 55 (15 - y)

W = 010 55 (y/3)2 (15 - y) dy

    = 010 (55/9) (15y2 - y3) dy

= [ (55/9) (5y3 - y4/4) ]010

    = [(55/9) {(5*103 - 104/4) - 0}]

W = (137500/9) ft - lb = 15277.78 ft - lb

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