A vertical right circular cylindrical tank has height \( h=5 \) feet and radius \( r=2 \) feet. It is filled with oil weighing 100 pounds per cubic foot.

How much work, \( W \) (in ft-lbs), does it take to pump all the oil from the tank to an outlet that is 3 feet above the top of the tank?

Answer

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Answer

\( W = \int_{0}^{5} (100\cdot\pi\cdot2^2) (5 + 3 - y) dy \)

Steps

Step 1 ：\( V = \pi r^2 h \)

Step 2 ：\( W = \int_{0}^{h} (100 \cdot V) (h + 3 - y) dy \)

Step 3 ：\( W = \int_{0}^{5} (100\cdot\pi\cdot2^2) (5 + 3 - y) dy \)