Cone Volumes

Fach:

Schlagwörter Functions, Surface area, Pythagoras, Triangle, Cones, Trigonometry, Volume

Calculate and optimise the volume of a cone using a variety of measurements. (OS 3.x)

Cone Volumes

Fach:

Schlagwörter Functions, Surface area, Pythagoras, Triangle, Cones, Trigonometry, Volume

Calculate and optimise the volume of a cone using a variety of measurements. (OS 3.x)

The aim of this activity is to have students work out the volume of a cone using a variety of different known measurements. This involves application of Pythagoras’ Theorem, and right-angled triangle Trigonometry.

Then the students progress to finding the optimum apex angle to maximise the volume of a cone for a given slant height. **No knowledge of calculus is required** – the process is completed using numeric Graph Analysis tools.

This activity is designed for students aged 12 to 15, both as a consolidating activity of existing skills and preparing the conceptual way for future optimisation problems.

The activity is structured as follows:

- Introductions and Assumptions.
*Checks prior knowledge.* - Focussing on using the Apex Angle.
*Two contexts and a 3D model are used.* - Optimising the Cone Volume.
*For a fixed slant height and variable apex angle.* - Light-Hearted Ending, with extension task.

*Although the screenshots displayed here are taken from a colour screen Nspire CX, the activity works just as well on a greyscale Nspire handheld. However, OS 3.0.2 or later is required.*