Need help finding the minimum surface area of a cylinder?

In summary, the student was warned about posting without showing an effort. They were given equations for the surface area and volume of a cylinder, but they were not correct. The student was asked to solve for the height and plug that into the surface area equation. Hopefully this helped.
  • #1
Sharni Kelaart
3
0
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

 
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  • #2
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
ehild said:
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.
 
  • #4
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
ehild said:
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
 
  • #6
How did you get those numbers?
 
  • #7
Since the OP has not provided a statement of the problem or any efforts toward solving it, I am closing this thread.
 
  • #8
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
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
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
 

Related to Need help finding the minimum surface area of a cylinder?

1. How do I find the minimum surface area of a cylinder?

To find the minimum surface area of a cylinder, you need to use the formula A = 2πr² + 2πrh, where r is the radius of the cylinder and h is the height. You can then use calculus to find the critical points and determine which one gives the minimum surface area.

2. What is the minimum surface area of a cylinder?

The minimum surface area of a cylinder will depend on the specific dimensions of the cylinder. However, using the formula A = 2πr² + 2πrh, you can calculate the minimum surface area for any given radius and height.

3. Can I use a different formula to find the minimum surface area of a cylinder?

While there may be other formulas that can be used to find the surface area of a cylinder, the formula A = 2πr² + 2πrh is the most commonly used and accepted formula for finding the minimum surface area of a cylinder.

4. What is the significance of finding the minimum surface area of a cylinder?

Finding the minimum surface area of a cylinder is important in applications such as manufacturing or packaging, where minimizing surface area can lead to cost savings. It also helps in optimizing the design of structures or objects that have a cylindrical shape.

5. How can I apply the concept of minimum surface area of a cylinder in real life?

The concept of minimum surface area of a cylinder can be applied in various fields such as architecture, engineering, and design. For example, when designing a water tank, finding the minimum surface area can help in determining the most efficient use of materials and reducing construction costs.

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