Pumping Problem

1. Mar 18, 2009

blessedcurse

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

3. 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!