THEORY:

Solid

A solid is a 3-D object having length, breadth, and thickness and bounded by surfaces that may be either plane or curved, or a combination of the two.
Solids are classified under two main headings

• Polyhedron

• Solids of revolution

A regular polyhedron is solidly bounded only by plane surfaces (faces). Its faces are formed by regular polygons of the same size and all dihedral angles are equal.  when faces of a polyhedron are not formed by equal identical faces, they may be classified into prisms and pyramids.

Tetrahedron: 4 equal equilateral triangular faces.

Cube(Hexahedron): 6 equal square faces.

Octahedron: 8 equal equilateral triangular faces.

Dodecahedron: 12 equal regular pentagon faces

Icosahedron: 20 equal triangular faces.

Prism

Prisms are polyhedrons formed by two equal parallel regular polygons, end faces connected by side faces which are either rectangles or parallelograms.

Some definitions regarding prisms

Base and lateral faces.  When the prism is placed vertically on one of its end faces, the end face on which the prism rests is called the base.

Base edge/Shorter edge: These are the sides of the end faces

Axis – it is the imaginary line connecting the end faces is called the axis

Longer edge/lateral edges: These are the edges connecting the respective corners of the two end faces.

Right Prism: A prism whose axis is perpendicular to its end face is called a right prism. Prisms are named according to the shape of their end faces, i.e, if end faces are triangular, the prism is called a triangular prism.

Oblique prism: It is the prism in which the axis is inclined to its base.

Pyramids
The pyramid is a polyhedron formed by a plane surface as its base and several triangles as its side face, all meeting at a point, called vertex or apex.

Axis: The imaginary line connecting the apex and the center of the base.

Inclined/slant faces: Inclined triangular side faces.

Inclined/slant/longer edges: The edges which connect the apex and the base corners.

Right pyramid: When the axis of the pyramid is perpendicular to its base.

Oblique pyramid: When the axis of the pyramid is inclined to its base.

Solids of revolution

when some of the plane figures are revolved about one of their sides – solids of revolution is generated some of the solids of revolution are:

1. Cylinder:  when a rectangle is revolved about one of its sides, the other parallel side generates a cylinder.

2. Cone: when a right triangle is revolved about one of its sides, the hypotenuse of the right triangle generates a cone.

3. Oblique cylinder: when a parallelogram is revolved about one of its sides, the other parallel side generates a cylinder.

4. Sphere:  when a semi-circle is revolved about one of its diameters, a sphere is generated.

5. Truncated and frustums of solids – when prisms, pyramids, cylinders are cut by cutting planes, the lower portion of the solids (without their top portions) are called, either truncated or frustum of these solids.