**Prerequisites:** Riemann Sums, Definition of Definite Integral

**Goal:** To discover a method to evaluate the volume of a solid of rotation

- How is the bottom left graph related to the top left graph? In particular, what concept does the bottom left graph demonstrate about the top left graph?
- How is the top right graph related to the top left graph?
- How is the bottom right graph related to the top right graph? In particular, what concept does the bottom right graph demonstrate about the top right graph?
- Consider the
*i*rectangle in the bottom left graph.^{th}`a.`If the midpoint of the interval is*x*, what is the height of the rectangle?_{i}^{*}`b.`What is its width? Hint: we had a short-hand notation for this.`c.`What is its area?

- Write a Riemann Sum for the area of the bottom left graph. Use
*n*for the number of sub-intervals. - Write a Definite Integral for the area of the top left graph.
- Consider the
*i*cylinder in the bottom right graph.^{th}`a.`If the midpoint of the interval is*x*, what is the radius of the cylinder?_{i}`b.`What is the area of a cross section of the cylinder?`c.`What is the thickness of the cylinder? Hint: we can recycle short-hand notations.`d.`What is its volume?

- Write a Riemann Sum for the volume of the bottom right graph. Use
*n*for the number of sub-intervals. - Write a Definite Integral for the volume of the top right graph.