A cylindrical can with height h and radius r is to be made to hold 1L (i.e. 1000cm3)of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can.

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Formula for the volume of the cylinder is `V=r^2 pi h` which is equal to 1. From that we conclude that

`h=V/(r^2pi)=1/(r^2pi) `    (1)

Surface area of the cylinder (which we must minimize) is given by formula `S=2r^2pi+2rpih` ` `

Now we plug formula (1) into formula for surface area to get

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