It is usually easiest to define a coordinate system in which as many variables
as possible will be constant. Expressing a sphere in a cylindrical coordinates
requires using two of the three coordinates:
where k is some constant. This is simpler than
a sphere in Cartesian coordinates, but it is still not the best answer.
The
Project Links Glossary
has an entry on
Cylindrical coordinates
for those who are not very familiar with it.