It's test time! Determine your class's understanding of the topics of volume and cross sections with a thorough assessment on volume, area, and geometric shapes.

What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...

Review the principles of scaling areas and draws a comparison to scaling volumes with a third dimensional measurement. The exercises continue with what happens to the volume if the dimensions are not multiplied by the same...

Lead a discussion on the similarities between the properties of area and the properties of volume. Using upper and lower approximations, pupils arrive at the formula for the volume of a general cylinder. 

Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...

How do 2-D properties relate in 3-D? Lead the class in a discussion on how to draw and see relationships of lines and planes in three dimensions. The ability to see these relationships is critical to the further study of volume and...

If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...

Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two...

So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the instructional activity develops the definition of a general cylinder. Scholars continue on to develop a...

Use this activity on cross-sections of three-dimensional shapes in your math class to work on algebra or geometry Common Core standards. The lesson includes a list of relevent terminology, and a step-by-step process to illustrate the...

This resource allows users to test their geometry knowledge.

This is a detailed site with numerous links related to polyhedrons, the site explains the term polyhedron in terms of geometry and algebraic topology it briefly discusses special polyhedrons which link to other Math World sites which...

This MathWorld site shows pictures of polyhedra which can fill space. A discussion of these figures follows.

This question and answer site provides a lot of basic information about polyhedra. The five regular polyhedra, "The Platonic Solids," are described.

Use this site to discover how we represent higher dimensional objects in mathematics and how one might draw a four dimensional object on two dimensional paper and modeling fourth degree tetrahedron.

Math World site offers the definition of frustum and links to view a frustum of a pyramid, cone, and sphere.