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

[Beamsbox]

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.

 

[LCKurtz]

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.