SUMMARY
Background: Guy Brousseau’s theory of didactic situations has been considered an apparatus for the methodological structuring of didactic sequences configured in didactic and adidactic situations. Objectives: To investigate the contributions of the theory of didactic situations to the study of round bodies, focused on a praxis that meaningfully consolidates knowledge for the students. Design: We propose solving problem situations concerning the calculus of surface areas and volumes of round bodies using Cavalieri’s principle and Pappus’s theorems. Setting and participants: The research was conducted with two high school third-grade classes of a state institute of education located in the municipality of Júlio de Castilhos, RS, Brazil, with the participation of 25 students. Data collection and analysis: It was carried out through activities developed in the classroom and feedback given through Google Classroom. It was subsidised by the documental transcription of students’ records. Results: The research indicated that the didactic sequence development favoured intellectual autonomy and meaningful learning about the object of knowledge. Conclusions: The theory of didactic situations provided important subsidies for didactic organisation and analysis of the knowledge consolidation process involving the study of round bodies, indicating its application in the study of other mathematical objects in high school and higher education.