Volumes of Revolution
Students can explore volumes of revolution visually using a prepared TI-Nspire document which leads them, step by step, through the process of deriving the standard formula for finding the volume of the generated shape.
They explore how the volume can be approximated by slicing the shape into a series of thin cylinders and finding the sum of their volumes. Students then see how this approximate volume can be made more accurate by increasing the number of slices. Then, after taking the limit of the total volume as the number of slices is increased to infinity, an integral is introduced.
Finally students are able to examine under what circumstances the approximation is an overestimate of the true volume and under which it is an underestimate.
The TI-Nspire document gives students full instructions and also encourages them to reflect on their exploration. There are three pages of notes for teachers.