Pumping Problem (1 Viewer)

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1. The problem statement, all variables and given/known data

A tank is in the shape of an inverted right circular cone with a radius of 10 feet and a height of 6 feet. Assume the tank contains water to a depth of 4 feet. Find the work required to pump all but 1 foot of water from the tank.

2. Relevant equations

W=[tex]\int^{b}_{a}Fdx[/tex]
F= weight*[tex]\Delta[/tex]v
[tex]\Delta[/tex]v=[tex]\pi[/tex]r[tex]^{2}[/tex][tex]\Delta[/tex]y
weight of water=62.4 ft/lb

3. The attempt at a solution

[tex]\Delta[/tex]v=[tex]\pi[/tex](5y/3)[tex]^{2}[/tex][tex]\Delta[/tex]y
[tex]\Delta[/tex]v=25[tex]\pi[/tex]/9*y[tex]^{2}[/tex][tex]\Delta[/tex]y

F=62.4*25[tex]\pi[/tex]/9*y[tex]^{2}[/tex][tex]\Delta[/tex]y
F=544.54y[tex]^{2}[/tex][tex]\Delta[/tex]y

W=[tex]\int^{6}_{1}544.54y^{2}(6-y)dy[/tex]
W=[tex]\int^{6}_{1}3267.26y^{2}-544.54y^{3}dy[/tex]
W=[tex][1089.09y^{3}-136.14y^{4}]^{6}_{1}[/tex]
W=235242.46-176431.84-1089.09+136.14

W=57857.67 ft*lb

Did I do my work correctly? Help please! Thank you much!
 

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