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    Minimum 2

    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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    Quote Originally Posted by deltaX View Post
    What is the radius of a cylindrical soda can with volume of 512 cubic inches that will use the minimum material?
    $\displaystyle 512 = \pi r^2 h$

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

    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
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