Dionysodorus is remembered for solving the cubic equation by means of the intersection of a rectangular hyperbola and a parabola. Eutocius credits Dionysodorus with the method of cutting a sphere into a given ration, as described by him. Heron mentions a work by Dionysauras entitled On the Tore, in which the volume of a torus is calculated and found to be equal to the area of the generating circle multiplied by the circumference of the circle created by tracing the center of the generating circle as it rotates about the torus's axis of revolution. Dionysodorus used Archimedes' methods to prove this result.
It is also likely that this Dionysodorus invented the conical sundial.