# Thread: Work: The Pool Problem

1. ## Work: The Pool Problem

1. The problem statement, all variables and given/known data
A circular swimming pool has a diameter of 22 ft, the sides are 5 ft high, and the depth of the water is 4 ft. How much work is required to pump all of the water over the side? (Use the fact that water weighs 62.5 lb/ft^3.)

(a) Show how to approximate the required work by a Riemann sum. Give your answer using the form below. (If you need to enter -infinity or infinity, type -INFINITY or INFINITY.)

(b)Express the work as an integral and evaluate it.

3. The attempt at a solution
I've found everything in the riemann sum equation minus the "E". What would this be?
A=N
B=infinity
C=1
D=N
E=?

One I find that, I should be able to setup the integral and solve it.

Thanks!

2. The kth layer is a cylinder of radius 11 and height $\displaystyle {\Delta}x_{k}$

the force required to move it is $\displaystyle ({\pi}r^{2}{\Delta}x_{k})\cdot[\text{weigth density of water}]$

The work needed to pump the kth layer of the edge of the pool would be

$\displaystyle W_{k}=(5-x_{k})\cdot{62.5{\pi}(121)}{\Delta{x_{k}}}$

$\displaystyle \frac{15125\pi}{2}\int_{0}^{4}(5-x)dx$

3. So what is E in the reimann sum? I've entered everything, but came up with no correct answer.

Thank you Galactus, you explain the problem so it actually makes sense!