Volumes of Revolution
applied
A classic: What will be your take on this? - Explore the mathematical principles and create your own unique investigation.
Introduction
To determine the volume of an object with circular cross-sections, we can use the idea of volumes of revolution. The topic is no longer in SLAA but is accessible and can be interesting. Fit the object with a piecewise function and model the volume on GeoGebra. Determine the curves with different methods and compare accuracy. The challenge will be to make your approach interesting and mathematically meaningful.
Guiding Questions
- What geometric shapes are involved?
- How can you express the volume as a function?
- Can you use calculus (integration) to find exact volumes?
- How do parameter changes affect the volume?
- What assumptions and approximations are you making?
Key Mathematical Concepts
3D Geometry
Calculus
Integration
Volumes of Revolution