Why do we need the derivative for the surface area? (English)

PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 5, 393-405 (2016).

Summary: Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric observations and the Squeeze Theorem.