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Volume of the space region inside sphere outside coni

  1. May 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi everybody i have a problem please help me (sorry for my bad english)

    2. Relevant equations
    volume of the space region inside sphere outside coni
    z^2=x^2+y^2 coni
    x^2+y^2+z^2 =1 sphere

    3. The attempt at a solution
    I am new in this forum , I search question like this and i found but i didn't solve this question with method that is performed other questions
     
  2. jcsd
  3. May 13, 2012 #2

    sharks

    User Avatar
    Gold Member

    Hi melihaltintas

    First, always plot the graph so you can understand how to find the limits.

    I have attached the graph of the xz-trace coordinates (in the plane y = 0). The region of volume that you need to find is shaded in blue.

    Start by finding the points of intersection of the sphere and cones (in the plane y = 0).

    Your equations for the cones and sphere in the plane y = 0, become:
    [tex]z^2=x^2
    \\x^2+z^2 =1[/tex]
    Solve these two equations to find the x and z. From there, you'll be able to find the two required angles for ##\phi## which define the limits.

    Finally, use the triple integral formula in terms of spherical coordinates:
    [tex]\int \int \int \rho^2 \sin \phi d\rho d\phi d\theta[/tex]
     

    Attached Files:

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    Last edited: May 13, 2012
  4. May 13, 2012 #3
    thanks a lot :)
     
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