Design a Better Drink Can
Adapted from an algebraic modelling activity on the HSC Online website. A standard can of drink holds 375 ml.Most are around 6cm across the base, and 13 cm high. But is this the BEST size? Since the cost of materials is most closely related to the surface area of the can, we would like dimensions that give the greatest volume for the smallest surface area. Drag the point shown to change the radius and observe the graph to see how the surface area (divided by 100!) changes! Try different volumes.
Try and find the algebraic function which matches this situation. Steve Arnold, 15/10/2006, Created with GeoGebra 
This problem may also be modelled using CabriJr on the TI83/84 series calculator. Click on the graphic below to download the file and try it yourself! Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model! 
And just wait until you try this with TInspire CAS! 
I decided to extend this problem a little further, and found that I had five different can sizes in my pantry! (Note that my data opposite includes a can of soft drink which is not shown). Can you pick the odd one out? Are any of these cans optimal? 

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