Final answer:
The shape of a shell with an inner radius of a and an outer radius of b is a sphere, not a cylinder, cone, or cube. This geometry is relevant to the study of electric fields and capacitors in physics.
Step-by-step explanation:
The shape of the shell described as thick and having an inner radius of a and an outer radius of b is a sphere. When we talk about a shell in geometry that has an inner and an outer radius, we're referring to a hollow object and, in this case, one that is spherical. The description does not match that of a cylinder, cone, or cube, as spheres are unique in their set of symmetrical properties, having all points on their surface equidistant from a central point.
Several examples in physical applications involve concentric spherical shells, such as in the study of electric fields and capacitors. A metallic spherical shell carrying a charge, for instance, will influence the electric field distribution within and outside of the shell, pertinent to several of the students' questions here.