# Finding the value of variables

• Jan 21st 2014, 07:51 PM
Tren301
Finding the value of variables
Hi there,
I have a question I'd like some help with please. I need to find the values for r and h in a cylinder. I have the volume from which to work. This needs to be plotted in an x, y graph I think, and then to find the smallest SA for this volume. See attachment.

Any help much appreciated

(Happy)
• Jan 21st 2014, 08:39 PM
romsek
Re: Finding the value of variables
Quote:

Originally Posted by Tren301
Hi there,
I have a question I'd like some help with please. I need to find the values for r and h in a cylinder. I have the volume from which to work. This needs to be plotted in an x, y graph I think, and then to find the smallest SA for this volume. See attachment.

Any help much appreciated

(Happy)

$\displaystyle V=\pi r^2 h$

$\displaystyle A=2\pi r^2 + 2\pi r h$

solving for h from the Volume equation

$\displaystyle h=\frac{V}{\pi r^2}$

plugging that into the Surface Area equation

$\displaystyle A=2\pi r^2 + 2\pi r \left(\frac{V}{\pi r^2}\right)=2\pi r^2 + \frac{2V}{r}$

now plug in the fact that V=375 ml

$\displaystyle A=2\pi r^2 + \frac{750}{r}$

now go to wolframalpha.com (or use your favorite graphing software) to plot this expression for the Surface area.

Put "Plot[2 pi r^2 + 750/r,{r,2,6}]" into wolframalpha.com to get a plot.

see if you can take it from here.
• Jan 21st 2014, 09:29 PM
Tren301
Re: Finding the value of variables
I graphed it on my calculator, it comes out as a reciprocal function graph. I graphed the volume function as well, and looked for an intersection. I thought this would tell me the answers for radius and volume. I looked at the answers radius=3.9, height=7.8. But it doesn't match my graph intersections. What am I missing here?

Thanks
• Jan 21st 2014, 10:05 PM
romsek
Re: Finding the value of variables
Quote:

Originally Posted by Tren301
I graphed it on my calculator, it comes out as a reciprocal function graph. I graphed the volume function as well, and looked for an intersection. I thought this would tell me the answers for radius and volume. I looked at the answers radius=3.9, height=7.8. But it doesn't match my graph intersections. What am I missing here?

Thanks

I don't know what you mean by a reciprocal function.

If you plot this like I said you can see the minimum lies around $\displaystyle r \approx 3.9$ and then you can use that value to find h in

$\displaystyle h=\frac{V}{\pi r^2}=\frac{375}{\pi (3.9)^2}\approx 7.8$
• Jan 21st 2014, 10:33 PM
Tren301
Re: Finding the value of variables
Thanks Romsek. Yes, It's not a reciprocal function as it curves up again away from the x axis. I must have typo'd the formula before because it worked straight up on my calculator this time and on Wolfram. (I need to pay for interactivity on Wolfram...it would be worth it though if I didn't have a good calculator. It certainly points one in the right direction as it is. I like it. Thanks for the referral. My calculator gave me ~3.9 this time. Thanks for your considerations.
• Jan 21st 2014, 11:12 PM
romsek
Re: Finding the value of variables
I see. I didn't realize they make folks pay for their website usage. Well I'm glad you got it figured out.