You are designing a $1000c{m}^{3}$ right circular cylindrical can whose manufacture will take waste into account. There is no waste in cutting the aluminum for the side, but the top and bottom of radius r will be cut from squares that measure 2r units on a side. The total amount of aluminum used up by the can will therefore be

$A=8{r}^{2}+2\pi rh$

What is the ratio now of h to r for the most economical can?

What is the ratio now of h to r for the most economical can?