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Intersection of a sphere and a cone. (projection onto the xy-plane)

  1. Dec 2, 2011 #1
    Part of a chapter review problem.

    Say you have a sphere centered at the origin and of radius 'a'.

    And you have a (ice-cream) cone which has it's point at the origin and phi equal to ∏/3.

    How do I find the equation of their intersection? Which is the projection onto the xy plane.

    Basically, I have to find the volume of the cone given the radius of the sphere (curvature of ice-cream) and phi = ∏/3... My answer needs to be in polar form, so I need to find the region of the projection, which has the same equation as their intersection, where z=0....


    Now I'm confusing myself... Any help would be nice.

    Cheers.
     
  2. jcsd
  3. Dec 2, 2011 #2

    LCKurtz

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    Set the z value on the cone equal to the z value of the sphere. (Actually, the z2 values are easier). That will give you the xy equation of the projection onto the xy plane.
     
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