Objectives

• This will show students how to use regular prisms to derive the formula to calculate the volume of a cylinder. Students will learn by visualizing how a regular prism will approach a cylinder as the number of the sides of the prism base increases to infinity.
• By now, the students should have learned how to calculate the volume of any regular prism. Therefore, we use a regular prism to approach a cylinder and use the volume of a regular prism to approximate the volume of a cylinder.
• As the experiment shows, the regular prism will become a perfect cylinder when the number of the base sides approaches infinity. Thus, its volume approaches the volume of the cylinder.

User´s Guide

1. Use the slider bar "Circle Radius" to change the radius of the cylinder base to a desired value.
2. Use the slide bar "Polygon Sides" to change the number of the sides of the prism base.
3. Use the button "Keep data" to permanently display the volume of the current regular prism on screen. The volume of the cylinder is always displayed on screen.

1. The starting prism is a regular 5-sided prism. Click the button "Keep data" to save its volume;

   Drag the slider "Polygon Sides" toward the center. Save two or three pieces of data along the way;

   Now drag the slider all the way to the maximum and save the data. Can you see how the volumes of regular prisms approach the volume of the cylinder?

    

2. Adjust the radius of the cylinder base to a new value and repeat step 1 through 3.