Need help finding the minimum surface area of a cylinder?

[Sharni Kelaart]

Member warned about posting without showing an effort
1. Homework Statement
'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?

Homework Equations

The Attempt at a Solution

 

[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.

 

[Sharni Kelaart]

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.

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.

 

[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?

 

[Sharni Kelaart]

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?

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

 

[ehild]

How did you get those numbers?

 

[Mark44]

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

 

[Mark44]

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.

 

[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

 

[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