Applied max/min Problem!! (Modern frozen juice packaging)

math_123

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Hello. Ive got problem in one of the applied max/min questions. Please anyone try helping me out :(

Question: Modern frozen juice packaging often uses paper for the sides and metal for the top and bottom of the container. Suppose the paper costs only 1/3 as much as the metal and that the can contains 270 cubic centimeters of frozen juice concentrate.

Find the dimensions (radius and height) of the most economical can. Give your answer to 2 D.P

volume of cylinder= pir r ^2h
surface area= 2 pir r^2 + 2 pie r h
 
That's a good problem. Feel free to show your personal efforts.
 
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