Superfícies e sólidos esféricos

Abstract

We present in this work strategies to determine the relationships for calculating the sphere volume and the spherical surface area. Some of these strategies depend on an intuitive notion of limit, but all of them are independent of notions of differential and integral calculus and can be adapted by the mathematics teacher for use in High School. In one of the strategies for the sphere volume, we employed the method of exhaustion inscribing straight truncated cones of parallel bases into the semisphere. Unlike the literature on the subject, which deals the method of exhaustion with inscribed cylinders in the semisphere, the methodology we describe leads to a finite numerical series whose limit we prove using the squeeze theorem. In addition, we mention daily life applications of the theme and describe three activities for the classroom about sphere volume, one of them with GeoGebra 3D. The work is interdisciplinary, associating algebra, geometry and number theory, and can be used by the mathematics teacher in Basic Education and also in Higher Education, especially in Mathematics Degree Course.