
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 14,279 Thanks: 1023 
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. 

Tags 
area, cylinder, height, radius, volume 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculate the radius of the cylinder if its height is 2.80m?  mathsheadache  Algebra  5  October 20th, 2014 07:38 PM 
Cylinder radius and height  Thepiman  Calculus  2  May 9th, 2014 06:16 AM 
Equilateral cylinder problem. Given radius, find...  gdirect  Algebra  3  December 11th, 2011 08:59 AM 
Really need help: volume, area of cylinder with derivatives  AFireInside  Calculus  1  September 10th, 2011 05:30 PM 
Need to find height of cylinder  manich44  Algebra  9  October 27th, 2009 02:15 AM 