# Minimum 2

• Mar 3rd 2010, 01:25 PM
deltaX
Minimum 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 PM
skeeter
Quote:

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