Volume of a particular snowcone.

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This 'snowcone' is different in that the cone is the paraboloid az=x^2+y^2and the top is the sphere x^2+y^2+z^2=2a^2. The circle of intersection becomes (x^2+y^2)/a = sqrt (2a^2-x^2-y^2). I can't proceed further to get the equation of the projected circle in the xy-plane. Any ideas?