Strategies for proving the volume of spheres in high school

• DOI: https://doi.org/10.22533/at.ed.5157125230072

• Palavras-chave: Archimedes' lever law. Cavalieri's principle. Mathematics teaching. GeoGebra 3D. BNCC.

• Keywords: Archimedes' lever law. Cavalieri's principle. Mathematics teaching. GeoGebra 3D. BNCC.

• Abstract:

  In this paper, we present two strategies for proving the relationship for calculating the volume of a sphere in high school: Cavalieri's principle and Archimedes' lever law. In Cavalieri's principle, we use the free software GeoGebra 3D to dynamically prove the relationship for the volume of a sphere; in the lever law or principle of equilibrium, we construct an Archimedes' balance with geometric solids made on a 3D printer to experimentally prove the relationship for the volume of a sphere. We conclude that the dynamic geometry application GeoGebra 3D is an effective tool for constructing two-dimensional and three-dimensional figures, as well as for comparing the areas and volumes of these figures, and that dynamic and experimental proofs enable the organization of classroom activities that address the competencies and skills outlined in the National Common Core Curriculum (BNCC) for mathematics teaching in high school.