### Home > PC3 > Chapter 10 > Lesson 10.1.2 > Problem10-32

10-32.

A company has $200 \text{ cm}^{2}$ of material to make an open cylindrical container (has a bottom but no top). How should they design the can so that it can hold as much as possible?

$\text{SA} = πr^{2} + 2πrh$
$\text{V} = πr^{2}h$

The volume needs to be maximized, so set the SA equal to $200$, solve for $h$, then substitute the result into the volume equation.

$h=\frac{200 - πr^{2}}{πr}$