Problem :
How does the length of the altitude of a cone compare to the length of
any of the segments that compose the lateral surface of the cone?
The altitude, because it is perpendicular to
the plane of the base, is always of
lesser or
equal length than the segments that make up the lateral surface.
Problem :
When is a cone a pyramid?
When the base is a polygon
Problem :
Does the altitude of a pyramid have to be in the interior of the pyramid?
No. The altitude can lie either in the pyramid, outside of the pyramid, or even
on the
pyramid. The altitude lies on the pyramid when the vertex can be
connected
to the polygon with a line perpendicular to
the
plane of the base. It all depends on where the vertex is fixed.