Resumen de Calculus of pasta, sausages, and bagels: can their surface areas be derivatives of their volumes?
The surface area of a sphere as a function of radius, r, is a derivative of the volume of the sphere, and a few other families of solids with this property are known. Sometimes, the derivative relationship can be reached with a tricky choice of size parameter r. This paper presents an activity for students that discovers three types of solids that satisfy the derivative relationship between the volume and the surface area with a ‘natural’ choice of r. It turns out that families of solids with a derivative relationship includes delicious sausages and bagels among other forms.
