Most efficient cost for a cylinder

[EricPowell]

Homework Statement

An open-topped cylinder is to have a volume of 250 cm³. The material for the bottom of the pot costs 4 cents per cm², and the material for the side of the pot costs 2 cents per cm². What dimensions will minimize the total cost of this pot?

The Attempt at a Solution

$$
A_{bottom}=πr^2
\\
C_{bottom}=4(πr^2)
$$

$$
A_{side}=2πrh
\\
C_{side}=2(2πrh)
$$

$$
V=πr^2h
\\
250=πr^2h
\\
h=\frac {250}{πr^2}
\\
∴C_{side}=2(2πr\frac {250}{πr^2})
$$

$$
C_{total}=4(πr^2+2(2πr\frac {250}{πr^2})
\\
\frac {d(C_{total})}{d(r)}=8πr-\frac{1000}{πr^3}
$$

Then I tried to use the first derivative test. I am stuck.

 

[EricPowell]

Uhh I messed something up there with itex.

 

[EricPowell]

I really messed up the formatting in that first post so it kind of looks like a mess. Until I figure that out, perhaps someone could point me in the right direction to solving the question?

 

[EricPowell]

Okay I think I fixed all the formatting. Silly me.

 

[EricPowell]

NEVERMIND. I figured out my silly error. It's all good now. Can I delete this thread?

 

[Mark44]

NEVERMIND. I figured out my silly error. It's all good now. Can I delete this thread?

We don't delete threads as a matter of course. Even though it's of no use to you now, others might find it helpful.