What is the radius of a cylindrical soda can with volume of 512 cubic inches that will use the minimum material?

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- Mar 3rd 2010, 01:25 PMdeltaXMinimum 2
What is the radius of a cylindrical soda can with volume of 512 cubic inches that will use the minimum material?

- Mar 3rd 2010, 01:43 PMskeeter
$\displaystyle 512 = \pi r^2 h$

$\displaystyle h = \frac{512}{\pi r^2}$

material required = total surface area of the cylinder ...

$\displaystyle A = 2\pi r^2 + 2\pi rh$

sub in the expression for $\displaystyle h$ given above to get $\displaystyle A$ in terms of $\displaystyle r$ only ...

find $\displaystyle \frac{dA}{dr}$ and minimize