Yes, a cone would fit such a description
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No, a cone is not a tetrahedron. A cone is a three-dimensional geometric shape with a circular base and a pointed vertex. A tetrahedron, on the other hand, is a four-sided polyhedron with triangular faces.
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.
In a right circular cone a line from the vertex to the center of the circular base is perpendicular to the base. In an oblique circular cone that same line will not be perpendicular.
A cone has a circular base.
Cone