Solids of Revolution – from the Integration of a given Functionto the Modelling of a Problem with the help of CAS and GeoGebra

Konferenzbeitrag

After the students in high school have learned to integrate a function, the calculation of the volume of a solid of revolution, like a rotated parabola, is taken as a good applied example. The next step is to calculate the volume of an object of reality which is interpreted as a solid of revolution of a given function f(x). The students do all these calculations in the same way and get the same result. Consequently the teachers can easily decide if a result is right or wrong. If the students have learned to work with a graphical or CAS calculator, they can calculate the volume of solids of revolution in reality by modelling a possible fitted function f(x). Every student has to decide which points of the curve that generates the solid of revolution can be taken and which function will suitably fit the curve. In Austrian high schools teachers use GeoGebra as a software which allows you to insert photographs or scanned material in the geometric window as a background picture. In this case the student and the teacher can control if the graph of the calculated function will fit the generating curve in a useful way.

Verweise und Beziehungen

• Erschienen in: Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 600 - 605
• Verwandtes Objekt und Literatur: urn:nbn:de:bsz:14-qucosa-79236 ; qucosa:1658

Klassifikation und Themen

• Thema: Mathematik

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Wurnig, Otto
• Ereignis: Herstellung
• (wer): HTW Dresden

Weitere Informationen

• URN: urn:nbn:de:bsz:14-qucosa-81160
• Letzte Aktualisierung: 14.03.2025, 08:15 MEZ