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Hemisphere pump problem

<Moderator's note: Moved from a technical forum and thus no template.>

> The tank (hemisphere) is full of water. Using the fact that the weight of water is 62.4 lb/ft3, find the work required to pump the water out of the outlet. The radius of the hemisphere is 10.

jSPxn.png


##V =\pi x^2 h##

using the equation of a sphere with a center in $\ (0,10)$

##\ x^2 + (y-10)^2 = 100##

##\ x^2 = 20y-y^2##

And the volume is:

##V =\pi (20y-y^2) \Delta y##

the force would be:

##F =62.4 \pi (20y-y^2) \Delta y##

And the distance as the image says is:

##d = (10-y)##

Finally the work would be:

##\int_0^{10} 62.4 \pi (20y-y^2) (10-y)\, dy##

And the answer gives me ## 156000 \pi## but according to my textbook the answer have to be ## 41600\pi##

what I'm doing wrong?
 

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LCKurtz

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I set it up a different way and got the same answer as you.
 

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