Numerical method help

• Mar 27th 2014, 03:26 PM
Numerical method help
I realised i posted my problem in the wrong thread.

i'm currently doing a maths assignment based on cans. However I'm already stuck on the third question "Use a numerical method to find the radius for which the area is a miniumum" I did get a formula for the total surface area of the can which is: 2πr^2 + 2V/r. Can someone help me out please?(Worried)
• Mar 27th 2014, 04:31 PM
romsek
Re: Numerical method help
Can you give an idea of how you are supposed to use numerical methods for this?

The general method is to equate the derivative of the surface area with respect to the radius to zero and solve for the radius.

When you do this you get a closed form solution for r that can be evaluated on any calculator.

Is there some other method your teacher has in mind?
• Mar 29th 2014, 02:29 PM
Re: Numerical method help
We have to use excel for this and create a graph after. The radius is a fixed value. I don't know what to do
• Mar 29th 2014, 03:13 PM
romsek
Re: Numerical method help
Quote:

We have to use excel for this and create a graph after. The radius is a fixed value. I don't know what to do

Well to do it numerically you're going to have to pick a number for the volume.

Then I'd put a list of radii in column A and plot the surface area according to your formula in column B.

Chart that. You'll be easily able to pick out the value of r in your list that makes the smallest surface area.

Without a better idea of what methods you have available to use I'm not sure how to suggest you go about finding the actual minimum.
• Mar 29th 2014, 06:20 PM
Re: Numerical method help
The volume is 300ml. so what i do is do the formula and chart it?
• Mar 29th 2014, 06:35 PM
HallsofIvy
Re: Numerical method help
If you are given that the volume is 300 ml (your original post did not say that the volume was constant) then, yes, you can use the formula you give, $\displaystyle A= 2\pi r^2+ 2\frac{V}{r}= 2\pi r^2+ \frac{600}{r}$.

Yes, you could graph that and "zoom" in on points were the area is maximum. Another way to do this is to differentiate the function, with respect to r, to get $\displaystyle 4\pi r- \frac{600}{r^2}$. Set that equal to 0 and solve $\displaystyle 4\pi r^3= 600$. I don't think you really need a numerical method to solve that.
• Mar 30th 2014, 12:21 PM
Re: Numerical method help
Quote:

Originally Posted by HallsofIvy
If you are given that the volume is 300 ml (your original post did not say that the volume was constant) then, yes, you can use the formula you give, $\displaystyle A= 2\pi r^2+ 2\frac{V}{r}= 2\pi r^2+ \frac{600}{r}$.

Yes, you could graph that and "zoom" in on points were the area is maximum. Another way to do this is to differentiate the function, with respect to r, to get $\displaystyle 4\pi r- \frac{600}{r^2}$. Set that equal to 0 and solve $\displaystyle 4\pi r^3= 600$. I don't think you really need a numerical method to solve that.

Thank you very much. This has really helped