What circular sector is to be cut out of a circle so that the remaining surface maximizes the volume of a symmetric upright cone with the same lateral surface? Geogebra vs. Mathematica (Study of Mathematical Software and Its Effective Use for Mathematics Education)

Abstract

The main trust of this invcstigation is to apply Geogcbra and Mathematica to calculate the central angle of a circular sector that is to bc cut out of a circle of a given radius so that the remaining surface area maximizes the volume of a circular symmetric upright cone with the same lateral surface area. Solving the proposed problem on two different parallel tracks applying these Computer Algebra Systems reveals the pros and cons of these two popular CASs. Utilizing the dynamic geometry of the former and its embedded CAS is compared to the sophisticated algebraic manipulation power of the latter. The investigation utilizes two and three dimensional visualization animations making the investigation comprehensive.