Cálculo de volume por fatiamento com o uso de materiais didáticos de manipulação no laboratório de ensino de Matemática

Abstract

The main objective of this work is to use the calculation of volume by slicing to calculate the volume of Manipulation Didactic Materials, among them, some geometric solids that are found in the Mathematics Teaching Laboratory and to compare the volume obtained with the volumes found by the formula geometry and by the insertion of liquid inside these solids. The methodology used in this research is characterized as a case study, with a qualitative approach and exploratory nature, in which we use as research instruments, geometric solids, books, dissertations and scientific articles, among others. The rationale is based on the studies of several authors, including: Eves (2004), Stewart (2013), Guidorizzi (2013), Dolce and Pompeo (2013). Initially, we address some considerations about the Mathematics Teaching Laboratory and Manipulable Didactic Materials and a brief history of Differential and Integral Calculus, highlighting some mathematical personalities that were of great relevance for the development of Calculus. Then, we discuss the volume method by slicing, the geometric formulas to calculate the volume, and how to obtain the volume by inserting liquid inside these solids. Finally, we checked the measurements of the solids and calculated the volumes by the three methods and performed the comparisons. This allowed us to observe that the values obtained are very close, so that we can use any of the methods and that, within the limitations of the measuring instruments, it is possible to reach increasingly refined values.