Students use known algebraic expressions for length elements \(d\ell\) to determine all simple scalar area \(dA\) and volume elements \(d\tau\) in cylindrical and spherical coordinates.
This activity is identical to Vector Surface and Volume Elements except uses a scalar approach to find surface, and volume elements.
Find the formulas for the differential surface \(dA\) and volume \(d\tau\) elements (little chopped pieces of the surface and/or volume) for a plane, for a finite cylinder (including the top and bottom), and for a hemisphere. Make sure to draw an appropriate figure.