1. ## Help with word problems please

A can is to be constructed in the form of a right circular cylinder. If it is to contain 128$\displaystyle pi cm^3$, what dimensions will require the least amount of material.

This is what I did:

$\displaystyle pir^2h = 128pi$
solved for h
$\displaystyle h = 128/r^2$
since
$\displaystyle 2pirh + 2pir^2 = surface area$
so
$\displaystyle 256pi/r + 2pir^2$
graphed it to find the min., but what I got requires r = 0, which can't be right?

2. Originally Posted by ggeek101
A can is to be constructed in the form of a right circular cylinder. If it is to contain 128$\displaystyle pi cm^3$, what dimensions will require the least amount of material.

This is what I did:

$\displaystyle pir^2h = 128pi$
solved for h
$\displaystyle h = 128/r^2$
since
$\displaystyle 2pirh + 2pir^2 = surface area$
so
$\displaystyle 256pi/r + 2pir^2$
graphed it to find the min., but what I got requires r = 0, which can't be right?
redo your graph ... mine shows the minimum to be close to r = 4