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April 16th, 2017, 05:58 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 120 Thanks: 2  Double Integration with Polar Coordinates
Find the volume inside both r = 1 and r^2 + z^2 = 4. Answer: 32 * pi/3  4 * sqrt(3) * pi This is what I came up but the result is only half of the correct anbswer.. Any tips would be much appreciated. 
April 16th, 2017, 06:21 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715 
basically you have a cylinder capped at both ends with a partial sphere $V = \displaystyle 2 \int_0^{2\pi} \int_0^1 \int_0^{\sqrt{3}}~r~ dz ~dr~d\theta + 2 \int_0^{2\pi} \int_0^1 \int_{\sqrt{3}}^{\sqrt{4r^2}}~r~ dz ~dr~d\theta $ 
April 17th, 2017, 04:55 PM  #3 
Senior Member Joined: Jan 2017 From: Toronto Posts: 120 Thanks: 2  Is there any free online polar coordinates 3D graphing tool?

April 17th, 2017, 06:02 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 
See the responses at your post 3D polar coordinates problem 

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coordinates, double, integration, polar 
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