Question
Asked Dec 10, 2019
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A cylindrical tank, laying on its side, with radius 10 feet and length 40 feet is completely filled with
water. Set up-BUT DO NOT EVALUATE- a definite integral for the work done in pumping the
water out of the spout which is 2 feet tall and is located on top of the tank (as shown). Water weighs
62.5 lbs/ft³.
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A cylindrical tank, laying on its side, with radius 10 feet and length 40 feet is completely filled with water. Set up-BUT DO NOT EVALUATE- a definite integral for the work done in pumping the water out of the spout which is 2 feet tall and is located on top of the tank (as shown). Water weighs 62.5 lbs/ft³.

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Expert Answer

Step 1

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The circular cross section has a radius 10 feet. | 2 ft dx 10-x 10 ft 10 ft The strip of width dx is x unit from top.

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Step 2

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10' = (10 – x )+(Horizontal length) Horizontal length = 100–(10–x) Total horizontal length becomes 2/100-(10 –x)' . Thus, the volume of the strip becomes 2,100 -(10-x)' ×40× dx. The value of x varies from 0 to 10.

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Step 3

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pxV =62.5×80,100 – (10 – x)´dx = 5000 100 – (10 – x) dr where p is the density of the water. The water has to be displaced through the sprout by s= x+ 2 ft.

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Advanced Math