Compare and contrast area and volume

Area is a region bounded by a CLOSED path, curved path or path with line segments.  Area is usually a two dimensional physical quantity, a designated part on a plane.  An example the surface of a table, face of a wall or a ceiling.  It can also be a surface in 3-dimensions.  Its units are meter² or centimeter² or feet²  etc. A large agricultural field is a good example of an area.  Normally and ideally no object can reside or exist with in an area. An object requires a volume.  It is a collection of all points enclosed or bounded by the boundary or closed path.  It does not have any thickness.

Volume is a 3-dimensional quantity. A physical body occupies space with its material components. It is the amount of space occupied, that is its volume. Any existing body occupying some space has a mass and volume.  A mass having a volume, has surface area and thickness, a height perpendicular to its surface at each point on the surface.
It is expressed as meter³, feet³ etc.
Volume is a product of surface area (cross-section) and length - for example for a wire or rod.