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.
  1. 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?
  2. 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?
  3. Check Show Graph, watch the animation of the liquid and how the graph of height vs volume is constructed?
  4. Explain why the graph looks like this shape
  5. (Extension) What type of graph is shown below? Can you determine this algebraically?
  6. How does the radius of the container affect the graph of the liquid's height?
  7. How does changing the container height affect the graph of the liquid's height?
  8. Would we expect the same graph for a Pyramid? Investigate the questions above for a pyramid as well.