Work needed to pump water to a tank

1. Feb 6, 2012

theBEAST

1. The problem statement, all variables and given/known data
I have attached the question with a diagram and answer key.

3. The attempt at a solution
What I did was found the work needed to pump the water into the bottom half of the sphere from 90-100 and then add that to the work needed to pump the water into the top half of the sphere.

integral from 0 to 10 9800pi(100-x^2)(90+x) + integral from 0 to 10 9800pi(100-x^2)(100+x)

When I plug in my numbers using wolfram I get:
http://www.wolframalpha.com/input/?i=integrate+from+0+to+10+(9800pi(100-h^2)(190+2h))

Which is slightly off compared to what the answer key gets:
http://www.wolframalpha.com/input/?i=integrate+from+-10+to+10+(9800pi(100+x)(100-x^2)

Does anyone know why they would be different? I feel like my logic is correct...

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2. Feb 6, 2012

susskind_leon

Your flaw is in your first integral. When x=0 (in the first integral), you're 90m above the ground. Yet, the diameter is 10m, when it should be 0m ;)