Given the frequent practical use of rotation areas, the paper proposes to study the methods for solving and determining the intersection of these rotation areas with various pipes, assimilated to the straight line. The areas considered for the study are the sphere, hyperboloid, ellipsoid and paraboloid. Thus, for the sphere are solved cases in which the straight line passes or not through the center of it, and for the hyperboloid cases when the straight line is or is not concurrent with its axis. When determining the points of intersection between the rotation areas and straight lines are used descriptive geometry methods, the method of auxiliary cone and Rouche’s method.
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