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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.