# Most efficient cost for a cylinder

1. Apr 28, 2013

### EricPowell

1. The problem statement, all variables and given/known data
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?

3. 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.

Last edited: Apr 28, 2013
2. Apr 28, 2013

### EricPowell

Uhh I messed something up there with itex.

3. Apr 28, 2013

### 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?

4. Apr 28, 2013

### EricPowell

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

5. Apr 28, 2013

### EricPowell

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

6. Apr 29, 2013

### Staff: Mentor

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.