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**1. 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?

**2. Homework Equations**

m = density*volume

**3. 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 (i

*th*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