The sphere and the pyramid: a dynamic construction proposal using Cavalieri's Principle

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DOI:

https://doi.org/10.23925/2237-9657.2023.v12i3p099-106

Keywords:

Cavalieri’s Principle, sphere, pyramid

Abstract

In this article we present a proposed activity involving GeoGebra and the Cavalieri’s Principle, which is a mathematical result that allows comparing cross-sectional areas and deducing volumes of solids. From the formula for the volume of a pyramid, it is possible to deduce the formula for the volume of the sphere. This is an unusual approach, since the pyramid is a solid with a surface consisting of flat faces, while the sphere is a solid with a non-flat surface.

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References

BRASIL. Ministério da Educação. Base Nacional Comum Curricular. Brasília: MEC, 2018.

GUIDORIZZI, H. L. Um Curso de Cálculo. Rio de Janeiro: LTC - Livros Técnicos e Científicos Editora. 5ª ed., v. 3. 2002.

LIMA, E. L.; CARVALHO, P. C. P.; WAGNER, E.; MORGADO, A. C. A Matemática do Ensino Médio. Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 6ª ed., v. 2 e v. 4. 2006.

SETTIMY, T. F. O.; BAIRRAL, M. A. Dificuldades envolvendo a visualização em geometria espacial. Vidya, v. 40, n. 1, jan./jun. 2020. p. 177-195.

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Published

2023-11-28

How to Cite

Agustini, E., Lopes, Érika M. C., & Pereira, G. M. R. (2023). The sphere and the pyramid: a dynamic construction proposal using Cavalieri’s Principle. Journal of the GeoGebra International Institute of São Paulo, 12(3), 0099–106. https://doi.org/10.23925/2237-9657.2023.v12i3p099-106

Issue

Vol. 12 No. 3 (2023): Volume 12, no. 3, 2023

Section

Proposals for Action

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