I'm having an extremely hard time trying to calculate the volume of the cone given by .

I've tried to draw it in the plane : its generators cross when , . In the plane its cross section is an ellipse centered at the origin, whose semi major axis is worth unit and its semi minor axis is worth . But I'm not sure I've done it right. Also I have a big problem : when using cylindrical coordinates, goes from to , goes from to but goes from to ... I'm unable to find it. I guess I must find some equation of generators, but still, the cone is not circular (cross section with the xy plane), making it difficult for me to find its volume.