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May 12th, 2015, 04:20 AM  #1 
Member Joined: Jun 2012 Posts: 73 Thanks: 2  Cylinder area through volume, radius, height
Hi, I want to express cylinders area through volume, diameter(or radius) and height. I found this equation: A = 1.845*(2+h/d)*(V**(2/3)) where: A  overall area of the cylinder h  cylinder height d  cylinder diameter V  cylinder volume However the upper formula is valid only for h=d (cylinder height = cylinder diameter). Does anyone know of some other formula for cylinder Area which is valid for any h/d ratio? Thank you. 
May 12th, 2015, 05:45 AM  #2 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
$\displaystyle V=\pi r^2h=r(\pi rh)=>\pi rh=\frac{V}{r}$ $\displaystyle V=\pi r^2h=(\pi r^2)h=>\pi r^2=\frac{V}{h}$ $\displaystyle A=2\pi rh+2\pi r^2=2(\pi rh+\pi r^2)=2(\frac{V}{r}+\frac{V}{h})$ 
May 12th, 2015, 09:34 AM  #3 
Member Joined: Jun 2012 Posts: 73 Thanks: 2 
Wonderful! Thank you Skaa. 
May 14th, 2015, 05:12 AM  #4 
Member Joined: Jun 2012 Posts: 73 Thanks: 2 
Would you mind if I ask one more question? Is it possible to express the cylinder area formula only through cylinder volume and radius/height (or diameter/height) ratio? For example I know the volume of the cylinder and radius/height ratio. How would the cylinder area formula look in that case? Thank you. 
May 14th, 2015, 10:37 AM  #5 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
Let's $\displaystyle \frac{r}{h}=q \Leftrightarrow r=hq \Leftrightarrow h=\frac{r}{q}$ . Then: $\displaystyle V=\frac{\pi r^3}{q} \Leftrightarrow r=\sqrt[3]{\frac{Vq}{\pi}}$ $\displaystyle V=\pi h^3q \Leftrightarrow h=\sqrt[3]{\frac{V}{\pi q^2}}$ So: $\displaystyle A=2\sqrt[3]{\frac{V^2\pi}{q}}(1+q)$ 
May 25th, 2015, 08:39 AM  #6 
Member Joined: Jun 2012 Posts: 73 Thanks: 2 
Thank you very much once again.

May 25th, 2015, 09:05 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 
Do you sell StGeorge wine? 
May 31st, 2015, 01:03 PM  #8 
Member Joined: Jun 2012 Posts: 73 Thanks: 2 
Not really Denis The "St" is part of my Last name, but it's not "Saint". I wish I was one 
June 7th, 2015, 08:42 PM  #9 
Senior Member Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus 
its easy, volume is pi*r^2/h area is 2pi*r(h+r) now you can easily blend above two equations with little manipulation to get any result, its just a mathematical manipulation.Though i cannot understand the relevance of expressing area by volume, its just like complicating simplicity. 

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area, cylinder, height, radius, volume 
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