Find Work to Pump Water from an Inverted Cone Tank

[blessedcurse]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

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

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

W=$$\int^{6}_{1}544.54y^{2}(6-y)dy$$
W=$$\int^{6}_{1}3267.26y^{2}-544.54y^{3}dy$$
W=$$[1089.09y^{3}-136.14y^{4}]^{6}_{1}$$
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!

 

[mighty2000]

I would suggest verifying your calculations and equations to ensure accuracy. It would also be helpful to provide units for each variable and to clearly define the limits of integration. Additionally, it may be beneficial to provide a diagram or visualization of the tank to better understand the problem. Overall, your approach seems reasonable, but it is always important to double check your work to ensure accuracy.