Prisms, Pyramids, Cylinders, and Cones
The Ultimate Goal: Find the Volume and Surface Area of Prisms, Pyramids, Cylinders, and Cones*
Finding the volume and surface area of prisms and pyramids is particularly interesting, and worthwhile for students, because it involves use of the Pythagorean theorem, modeling, visualization, measurement, and problem solving.
Here are some links to help see what's going on.
Here is my flowchart (.doc) showing a possible progression for teaching these concepts.
In my humble opinion: A big key to understanding volume and surface area is to understand the rectangular pyramid. It has three key “heights” and three key lengths on the rectangular base. This handout describes the "Essential Tetrahedron," whose 4 faces are all right triangles (made to order for the Pythagorean Theorem)!!
There is an Essential Tetrahedron for every pyramid with a polygonal base.
How to Build a 3D Model of a Pyramid
Click here for the steps on how to build a rectangular pyramid out of coffee stirrers (or straws) and fuzzy sticks (or chenille stems). (Click here for the steps on how to build a rectangular or square pyramid.)
Here's a video:
www.geogebra.org/en/upload/files/english/lewisprisco/nsf09cylinder_
worksheet.html
Online worksheet investigating volume and surface area of cylinders + answerswww.geogebra.org/en/upload/files/english/lewisprisco/rectangular_pyramid.html
Online worksheet investigating volume and surface area of rectangular pyramids + answerswww.geogebra.org/en/upload/files/english/lewisprisco/nsf09cone_worksheet
.html
Online worksheet investigating volume and surface area of cones + answerswww.geogebra.org/en/upload/files/english/lewisprisco/triangular_prism1.html
Online worksheet investigating volume of triangular prisms + answers
Square Pyramid and Its Right Triangles (especially #2, 3, 4, 8) from Wolfram Demonstrations Project: http://demonstrations.wolfram.com/SquarePyramidAndItsRightTriangles/
Three Pyramids That Form a Cube from Wolfram Demonstrations Project: http://demonstrations.wolfram.com/ThreePyramidsThatFormACube/
Miscellaneous volume and surface area worksheets online
*Spheres have been left off of this page and flowchart, but they could easily be added.
James R. Olsen, Western Illinois University
E-mail: jr-olsen 'at' wiu.edu
Page last updated:
September 16, 2012
