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...

Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from...

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...

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...

Using a similar process from the first activity in the series of finding area approximations, a measurement resource develops the proof of the area of a circle. The problem set contains a derivation of the proof of the circumference...

What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.

What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and...

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 lesson plan develops the definition of a general cylinder. Scholars continue on to develop a graphical...

As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal. 

An excellent resource for a geometry class, as well as for an electrical engineering course. A thorough reference sheet covers geometric shapes such as triangles, parallelograms, and circles, as well as 3-D shapes and the Pythagorean...

The history of math is fascinating! Utilize a woodcut primary source image from 1492 and posters from the 1930s to help geometers apply their volume-calculation skills to real-life questions. 

This site uses calculus to explain how the formulas for finding the volume of a sphere and a pyramid were derived.

This lesson focuses on the characteristics of a circle including similarity, radius, circumference, and Pi. It provides formulas to determine the area of a circle, calculating Pi, and learning exercises throughout.

This site provides the formula for circumference. Links are provided.

Find a quick, concise explanation of what a radius is. An example is given and clearly explained.

This question and answer site gives the formulas for area and volume of a cone.

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