Pouring Liquid into Cones and Pyramids
Students investigate the relationship between height and volume of cones and pyramids.
This is done through considering how the height of a liquid changes when poured into a cone or pyramid.
- Imagine a cone is filled up with water with pen and paper draw a graph of how you expect the height to change if the liquid was poured in at a constant rate?
- Empty the liquid from the cone, now fill the liquid. Upon viewing the 3D Graphic draw a graph that shows how the height changed relative to the volume of liquid poured?
- Check Show Graph, watch the animation of the liquid and how the graph of height vs volume is constructed?
- Explain why the graph looks like this shape
- (Extension) What type of graph is shown below? Can you determine this algebraically?
- How does the radius of the container affect the graph of the liquid's height?
- How does changing the container height affect the graph of the liquid's height?
- Would we expect the same graph for a Pyramid? Investigate the questions above for a pyramid as well.