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Basic Calculus volume question

  • Thread starter bopll
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  • #1
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Homework Statement



A water tank is in the shape of a half cylinder sitting on its side (not its top or its bottom). Let the radius be 10 ft and let the side-lenth on the floor be 30 feet. What should be the water height, measured from the floor up, so that the water tank is half full?

Homework Equations



Volume of a cylinder- h*(pi)r^2


The Attempt at a Solution



First i found the volume needed, which is (30)*(10)^2*pi/2 = 4712.4

Then I tried this problem breaking down rectangular boxes into dy components and set up the integral as follows (using 2sqrt(100-y^2 as the width of the boxes and y as the height of the boxes and 30 being the constant length)

30[tex]\int^{0}_{h}[/tex][tex]\2sqrt{100-y^{2}}[/tex]*2y dy

and set it equal to the needed volume.

I ended up getting 7.7, which i feel is wrong because the height should be less than half of the radius by just thinking about what SHOULD happen.

Should i be taking an entirely different approach to this or what?

ps sorry for the formatting inconsistencies... kinda new here.

thanks guys.

edit: i can't get my bounds right for whatever reason, but i set it from 0 to h.
 
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Answers and Replies

  • #2
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nevermind, i guess i did the calculations wrong.

Can anyone confirm this setup at least?
 
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