Chapter 10: Calculating the volume of a solid of revolution: From geometry to 3D impression

Teaching integral calculus in the early semesters of engineering programs represents a challenge, as students often perceive it as abstract and disconnected from real-world applications. To address this issue, the aim of this study was to design and implement an innovative didactic strategy that integrates geometric concepts, integral calculus, and digital tools to facilitate the understanding of volume calculation through solids of revolution. A qualitative and exploratory approach was applied through three classroom case studies in which students worked with scaled physical models, mathematical visualization software, and 3D prototyping. The results showed that the strategy strengthened students’ conceptual understanding, supported the validation of calculations, and fostered more meaningful learning by linking theory and practice. In conclusion, the experience demonstrated that the integration of manipulative, digital, and experimental resources contributes to the development of critical, visual, and spatial thinking, as well as key competencies for the comprehensive training of future engineers.