just found a really helpful sample problem online. thanks anyway.
might be posting another problem here in a few
ok, i drew out a diagram and I have no idea how or where to start this problem. Please help guide me so I can learn how to do it...
A water tank has the shape of an inverted circular cone with a diameter of 4 feet and a height of 6 feet. If the tank is full, find the work required to empty the tank through a pipe that extends 3 feet above the top of the tank. Use 62.5 as the weight-density of water. Give your answer in foot-pounds.
work = integral of WALT
W = weight-density in lbs per cubic foot
A = cross-sectional area of a representative horizontal "slice" of liquid in terms of y
L = lift distance of the representative "slice" in terms of y
T = "slice" thickness , dy.
let the vertex of the cone be at the origin ... one side of the cone is modeled by the linear equation ...
"slice" radius = , so the cross-sectional area of a representative "slice" is ,
lift distance,
the liquid resides between and ... your limits of integration.
set up the integral and find the work required.
thanks, ill be sure to remember WALT.
This is how I solved it, not 100% if its right but it seems it might be...
Weight of slab = density * volume
weight of slab = 500 pi dx
Distance = x + 3
Work = (x + 3)500pi dx
W = integral from 0 to 6 [(x+3)(500pi)]dx
W = 56,548.7 ft lbs