Polynomial Multiplication: Prism volume as the product of three given binomials defining the dimensions of a rectangular prism.

In this lesson you will learn the geometric intricacies to find prisms' volume as a function of a polynomial expression generated by the product of three binomial expressions describing the width, length, and height of a rectangular prism. Once one expression has been found, we may substitute values for "x" to find similar prisms (same shape different size.) Or substituting all three dimensions and the value for "x" and thus generate different prisms.

The activity involves foam and plastic base 10 blocks. It concludes with the application problem which may be modeled with two different transparent rectangular boxes and some fill-in material. Water heater liquid foam demos are online and may help to illustrate the idea in the problem. The problem is rich in a conceptual approach. Try to help yourself using the pen and highlighter in the MARKER TOOLS menu.

Lesson's Content

Lesson In PDF Format (no animations)


Lesson's Glossary

A segment that helps to make up a face.

A polygonal region of a surface.

Hidden lines
Broken lines used to signify lines that normally wouldn't be seen in a drawing.  

Lateral area.

Lateral area
The area of the lateral surface of a solid.

Lateral edge
A segment whose endpoints are corresponding points of a cylindrical solid's bases, or whose endpoints are the vertex of a conic solid and a vertex of its base.

Lateral faces
The faces of the lateral surface of a prism, or a face of a pyramid that is not a base.

Lateral surface
The surface not included in the base (s).

Oblique prism or cylinder
A non-right prism or cylinder.

A prism whose opposite faces are all parallelograms and congruent (in pairs).

A three-dimensional surface which is the union of polygonal regions and has no holes.

It is a polyhedron that has two congruent and parallel faces, called bases. The remaining faces, which are parallelograms are called lateral faces. The altitude is the perpendicular segment whose endpoints are at the bases. The length of the altitude is the height of the prism. A right prism is one with all lateral faces rectangles. An oblique rectangle has some to be nonrectangular.    

Right prism
A prism whose direction of sliding is perpendicular to the plane of the base.

The union of the surface and the region of space enclosed by a 3-D figure; examples: conic solid, cylindrical solid, rectangular solid.

Solid geometry
The study of figures in three-dimensional space.

The boundary of a 3-D figure.

Surface area
The total area of the surface of a solid.

Unit cube
Unit of measuring volume.

Factoring: The process to brake a polynomial down into the product of several factors.

Factors: All whole numbers that are multiplied together to yield another number.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Function: A relation of the type that has exactly one value in the domain (independent variable) matching a value in the range (dependent variable).

Function notation: A function written with the symbol f(x) instead of y. It is read as f of x.


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