# Need help finding the minimum surface area of a cylinder?

1. May 3, 2015

### Sharni Kelaart

Member warned about posting without showing an effort
1. The problem statement, all variables and given/known data

'Using the graphing function on your Graphics Calculator, or otherwise, determine the radius for a minimum Surface Area.' I HAVE NO IDEA WHAT TO DO??????????????

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 3, 2015
2. May 3, 2015

### ehild

Welcome to PF!

Type in the whole question, please. What else is given for the cylinder?
If nothing else is given, the minimum surface area belongs to zero radius, but I do not think that is the expected answer.

3. May 3, 2015

### Sharni Kelaart

Hi!
I have to do this for 3 different cylinders, and I've been given the volumes of each of them; 447.97cm, 153.94cm and 446.73cm.

4. May 3, 2015

### ehild

Well, you know the volume. How is it related to the radius r and the height h? What is the surface area in terms of r and h?

5. May 3, 2015

### Sharni Kelaart

I've worked the surface area of each of the cylinders to be (in terms of r only, as this is what was asked)
169.39cm
164.93cm
992.17cm

6. May 3, 2015

### ehild

How did you get those numbers?

7. May 3, 2015

### Staff: Mentor

Since the OP has not provided a statement of the problem or any efforts toward solving it, I am closing this thread.

8. May 3, 2015

### Staff: Mentor

Somewhat reluctantly, I'm going to reopen this thread. @Sharni Kelaart, this -- "I HAVE NO IDEA WHAT TO DO??????????????" -- does NOT constitute an attempt at a solution. In future posts, please make more of an effort to fill out the homework template.

9. May 3, 2015

### ehild

Sharni,

The rules here require that you explain what you think about the problem. You gave three numbers in your last post as result, have you got them from a plot on a graphing calculator? What was you plotted?

Next time when you start a thread obey the rules. Write the full text of the problem statement, write the formulae which can be relevant, ( they would be the volume and surface area of a cylinder here) and show what you think about a possible solution. In those equations, you have two variables, the radius r and the height h. You can eliminate one (h) and then you get a function, the area in terms of the radius. If I understand your post correctly, that was what you did and input the calculator. But the numbers are not correct. I would like to see that formula.

I hope to see you again soon.

ehild

10. May 4, 2015

### leafjerky

I don't know if you're still looking for help but...

Surface Area = 2πrh + 2πr2
Volume = πr2h

We have volume, but two unknown variables, radius and height.

Do you see how they are to be related?

We have to solve for h with the volume equation, then plug that h into surface area equation. I hope this is helpful. If you still don't get it, refer to this page: http://www.math-prof.com/Calculus_1/Calc_Ch_17.asp