There are 2 types of 3D solid geometry.

1. Polyhedra (all flat surfaces) - Platonic Solids, Pyramids and Prisms
2. Non-polyhedra (not all flat surfaces)

Here are some basic formulae to find the volume of the different 3D shapes. View it at this link: http://www.math.com/tables/geometry/volumes.htm Some terms:

Polyhedra: Has at least 1 face / side

Egs:

Polyhedra: Cube, Cuboid, Pyramid, Prisms, Cylinder

Non-Polyhedra: Sphere, Cone, Torus

Geometrically Similar: Same shape, different size. Ratio of respective dimensions are the same. ie. vol1/vol2 = length1/length2

Types of geometry:

Euclidean geometry: the lines remain at a constant distance from each other even if extended to infinity, and are known as parallel

Non-Euclidean (2types):

Hyperbolic geometry: lines "curve away" from each other, increasing in distance as one moves further from the points of intersection with the common perpendicular; these lines are often called ultraparallels.

Elliptic geometry: the lines "curve toward" each other and intersect.

Types of Solids:

Platonic Solids: Regular and convex polygon. Faces are congruent and meet each other at the same vertex.

Archimedian Solids: Distinct from platonic solids. They are symmetric, semi-regular and convex polyhedrons  composed of two or more types of regular polyhedrons meeting in identical vertices

Johnson Solids: Strictly convex polyhedron. They are platonic solids as well.