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.