Yes. A cone will roll following a circular path with the central axis being the point of intersection of the sides of the cone (which is the point of a pointed cone).
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A cone.
A cone
A cone-shaped object will not roll in a straight line because the circumference of the cone changes from one end to the other. For example, if one end of the cone has a circumference of 10 inches, that end will travel 10 inches per revolution, but if the other end of the cone has a 2 inch circumference, it will only travel 2 inches per revolution.