• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter cybermask
  • Start date
  • #1
5
0
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
 

Attachments

Last edited:

Answers and Replies

  • #2
5
0
I know that the mistake may be trivial but can anyone give me any comment!!!!!!!1
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618
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)?
 
Last edited:
  • #4
5
0
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
Science Advisor
Homework Helper
26,258
618
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
5
0
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
 

Related Threads for: Volume of the intersection of two cylinders by polar co-ordinates

Replies
7
Views
3K
  • Last Post
Replies
1
Views
15K
  • Last Post
Replies
16
Views
884
Replies
4
Views
1K
Replies
2
Views
8K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
19
Views
2K
  • Last Post
Replies
1
Views
942
Top