Objectives
- Application of the chain rule to related rates,
- Numeric and symbolic integration using technology
- Solids of revolution of a region about the coordinate axis
Vocabulary
Solid of revolution, rate, related rates
About the Lesson
Students start by sketching a graph that corresponds to a jug being filled. The YouTube video of the jug provides a timer and scale to measure the time and height with a good level of accuracy. An image is then used to assist students to model the shape of the vase, generate a function for the volume in terms of the height by using a solid or revolution. This 3D object is then used to validate the video observations. Finally, students use their function and rotated it around the z – axis to form a virtual 3D model of the vase!