# Really Urgent! derivative problems!

• Dec 17th 2008, 01:23 PM
Attack
Really Urgent! derivative problems!
I really need some help to solve this problem:

A factory are going to to make cylindershaped cans. The sum of the diameter and height are 80 cm. which measures gives the greatest volume?

Im sorry for it's a repost but it'll be handed in on a couple of eight hours of beaty sleep. So it would mean the world to me if someone could help me.
• Dec 17th 2008, 01:48 PM
skeeter
$d+h = 80$

$h = 80 - d$

$h = 80 - 2r$

$V = \pi r^2 h$

$V = \pi r^2(80 - 2r)$

$V = 2\pi(40r^2 - r^3)$

find $\frac{dV}{dr}$ and determine the value of $r$ (and hence, the value of $d$) that maximizes $V$.
• Dec 17th 2008, 01:57 PM
Attack
Well, I get 80r - 3r²

V'=0

80r=3r²

r=80/3

Is that correct? Or am I way out?