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Gauss177
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Homework Statement
A tank full of water has the shape of a parabloid of revolution with shape obtained by rotating a parabola about a vertical axis.
a) If its height is 4 ft and the radius at the top is 4 ft, find the work required to pump the water out of the tank.
b) After 4000 ft-lb of work has been done, what is the depth of the water remaining in the tank?
Homework Equations
m = density*volume
The Attempt at a Solution
I don't know how to do part (b). This is what I have for (a):
I labeled the radius of cross section as Ri (ith subinterval)
Ri/(4-Xi) = 4/4
Ri = 4-Xi
Volume of ith layer of water = pi(4-Xi)^2 dx
Mass of ith layer of water = 62.5pi(4-Xi)^2 dx
Force to raise ith layer = (9.8 m/s^2)(62.5pi(4-Xi)^2 dx
W to raise ith layer = 612.5pi*x*(4-x)^2 dx
Total work = Integral of 612.5pi*x*(4-x)^2 dx on [0, 4]
The answer is not right, so can anybody tell me what I did wrong and how to fix it? Also, how would you do part (b)?
Thanks