It could. If the nose is a right angle, it would be wide but a cone.
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Circle, cone, cylinder, sphere and equilateral triangle for example.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the result curve will be a parabola, unless the intersection includes the vertex of the cone, in which case the intersection is a straight line. This is a conic section. Depending on the angle of the plane, the section will be a circle, an ellipse, a parabola, or two hyperboles.
A right circular cone is perfectly balanced on its circular base. Imagine a cone that has a circular base, but leans to one side - this is a non right circular cone.
A right circular cone balanced on its apex.A right circular cone balanced on its apex.A right circular cone balanced on its apex.A right circular cone balanced on its apex.
In a right circular cone the apex is directly above the centre of the base.