Using polar coordinates to find the volume of the given solid

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  • #1
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1. Use polar coordinates to find the volume of the given solid.



2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
 

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  • #2
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1. Use polar coordinates to find the volume of the given solid.



2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
What have you tried? You have to show an effort first.
 
  • #3
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I've tried doing a double integral from theta=0 to theta=2pi and r=0 to r=4 of ((16-r^2)^(1/2))r (dr)(dtheta)
 
  • #4
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The limits of integration for r should be from r = 2 to r = 4. If you go from r = 0, you're getting the volume inside the cylinder, which you don't want.
 
  • #5
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Ok. Is the actual integral correct?
 
  • #6
34,675
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Yes, I don't see anything wrong with it.
 

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