There was three elements to this project. For the first, we had to find the volume of a bottle using equations to model it and then rotating it around one of the axes. The second part was designing a bottle that was between 500 and 600 ml. The third, and final, was to pick a bottle and redesign it, ending up with the same amount of fluid capacity. We had to create equations in the shape we wanted, and then using integrals, rotate it around the x-axis to find the volume. I chose a small powerade bottle. The redesigned bottle image is below along with the mathamatical work that went into it.
Topics Discussed:
- Review of Precalculus Skills
- Limits & Their Properties
- Differentiation
- Applications of Differentiation
- Integration
- Applications of Integration
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