How to minimize the amount of material used to make a shape of a given volume? A metal can company will make cylindrical shape cans of capacity 300 cubic centimeters. What is the bottom radius of the cans in order to use the least amount of the sheet metal in the production? Accurate to 2 decimal places.

Hint:


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*Write out the expressions for surface area and volume of cylinders. Here they are for reference:


$ A = 2 \pi  r h + 2 \pi r^2 $
$ V = \pi r^2 h $


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*We already know what the required volume is so we can set $ V = 300 $.

*Can we combine our expressions for $ A $ and $V $ and make progress that way?
ETA: curse my blurred vision!
