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April 16th, 2017, 05:58 PM   #1
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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.


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April 16th, 2017, 06:21 PM   #2
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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{4-r^2}}~r~ dz ~dr~d\theta $
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April 17th, 2017, 04:55 PM   #3
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Quote:
Originally Posted by romsek View Post
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{4-r^2}}~r~ dz ~dr~d\theta $
Is there any free online polar coordinates 3D graphing tool?
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April 17th, 2017, 06:02 PM   #4
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See the responses at your post
3D polar coordinates problem
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