Activity Overview
Liquid flows into a vase at a constant rate, sketch a graph of height vs time. Ever thought of actually doing this experiment to help students see that their sketch graphs really are correct? This activity links to a YouTube video so students can collect the data and use this to verify their sketch graph. The activity also includes modelling the curve and then eventually rotating it around the axis to produce a 3D image of the vase!
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!