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**[SOLVED] Work: Spherical Problem**

## Homework Statement

A tank is full of water. Find the work

*W*required to pump the water out of the spout. (Use 9.8 for

*g*and 3.14 for [PLAIN]http://www.webassign.net/images/pi.gif.[/URL] [Broken] Round your answer to three significant digits.)

*W=_________*

r=3

h=1

## The Attempt at a Solution

To set up this problem, I started by taking the area of one slice of water to be pi r[tex]^{2}[/tex] multiplied by an infitesimally small height [tex]\Delta y[/tex] to get volume. Then multiply this by the density of water; 1000 kg/m[tex]^{3}[/tex] to get the volume of one slice.

Now I want R as a function of, lets say y. We know the area of a circle is r[tex]^{2}[/tex]2+y[tex]^{2}[/tex]=3[tex]^{2}[/tex]. So r=sqrt(9-y[tex]^{2}[/tex]). Also, the distance for any slice from the top is 7-y.

After this I tried integrating from zero to six of the function 1000*pi*(9-y[tex]^{2}[/tex])*(7-y)*y. This came out to be negative....in fact -36000*pi..

Apparently, that is wrong. Where did I go wrong?

Thanks.

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