Stage: 4 Challenge Level: 
What are the most efficient proportions for a tin of paint?
"Efficient" could mean different things from different points of view - maybe start by trying to minimise the amount of material needed to make a tin with that volume.
What is the best diameter and height for a tin that contains $1$ litre of paint?
What about a $5$ litre tin?
Pythagoras' theorem. epsilons. Calculating with ratio & proportion. Index notation/Indices. Simultaneous equations. Ratio. Cylinders. Quadratic equations. Long problems. Surface and surface area.
Published February 2006.
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