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algol13
3 years ago
15

A tank in the shape of a right rectangular prism has a height of 5 feet, width of 3 feet, and length of 2 feet. It is full of a

liquid weighing 50 pounds per cubic foot. How much work does it take to pump all of the liquid out of the top of the tank

Mathematics
1 answer:
sveta [45]3 years ago
3 0

Answer:

Step-by-step explanation:

Given

height of tank h=5\ ft

Width of tank w=3\ ft

length of tank L=2\ ft

suppose a layer of water at height h of thickness dh from bottom needed to be pump out

So distance moved by this layer to come out of tank is \Delta h=5-h

weight density of water \rho =50\ pounds/ft

Force required to hold this layer up F_s=2\times 3\times \Delta h\times 50=300\Delta h

Work done to remove the water

W=\int_{0}^{5}300\Delta hdh

W=\int_{0}^{5}300\left ( 5-h\right )dh

W=3750\ Pound-ft

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