# Math Help - Minimum 2

1. ## Minimum 2

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

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

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

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

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

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

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