SOLUTION: Hello friends. I have a problem here that I am hoping someone can help me with . A right cylinder has a volume of 2pi cubic inches . Find the can dimensions that require the least

Question 962508: Hello friends. I have a problem here that I am hoping someone can help me with . A right cylinder has a volume of 2pi cubic inches . Find the can dimensions that require the least amount of aluminum to be used in the can construction? Thank you in advance !!!
Answer by hkwu(60) (Show Source): You can put this solution on YOUR website!
The volume is described by

The surface area is described by

Taking the derivative, we get

which is equal to zero when

If you do the first derivative test, you'll find that this is indeed a minimum value. Thus

so the optimal dimensions are 1in radius by 2in height.
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