Volume of the intersection of two cylinders by polar co-ordinates

  • Thread starter cybermask
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  • #1
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Volume of the intersection of two cylinders by cylinderical co-ordinates

Homework Statement




find Volume of the intersection of two cylinders by cylindrical co-ordinates


The Attempt at a Solution



IN the attached file I found it's 8(a^3)/3
It should be 16 not 8
 

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  • volume.pdf
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Answers and Replies

  • #2
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I know that the mistake may be trivial but can anyone give me any comment!!!!!!!1
 
  • #3
Dick
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Why do you think the upper limit of the dz integration is r*cos(theta)? Don't you have z=sqrt(a^2-y^2)=sqrt(a^2-r^2*sin(theta)^2)?
 
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  • #4
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Why do you think the upper limit of the dz integration is r*cos(theta)? Don't you have z=sqrt(a^2-y^2)=sqrt(a^2-r^2*sin(theta)^2)?

But in the first octent
x^2 + y^2 = r^2
y^2 + z^2 = r^2

so z=x=rcos(theta)

Isn't it?
 
  • #5
Dick
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That's only true along the curve where the two cylinders intersect. It's not true everywhere on the surface in the first octant.
 
  • #6
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That's only true along the curve where the two cylinders intersect. It's not true everywhere on the surface in the first octant.


Thanks Thanks Thanks
 

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