A complete lesson that completely covers the calculation of volumes by cross sections. Most calculus textbooks ignore this topic, or jump straight to very difficult examples.
This lesson begins with a review of geometry. Most calculus students have a difficult time writing an expression for the area of a cross section. This review eases them into it, from squares and rectangles up to equilateral triangles and semicircles.
There is one volume problem given that is meant to be worked through as a class, then a clear set of steps. Students then work through 6 practice problems. The handout is 6 pages in total.
Includes a complete answer key with all work shown. This lesson can be given before or after volumes by rotation. Excellent for AP Calculus AB or Calculus BC. I have used this lesson in both classes for several years with great success.