My Math Forum Cylinder area through volume, radius, height

 Geometry Geometry Math Forum

 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 $\displaystyle V=\pi r^2h=r(\pi rh)=>\pi rh=\frac{V}{r}$ $\displaystyle V=\pi r^2h=(\pi r^2)h=>\pi r^2=\frac{V}{h}$ $\displaystyle A=2\pi rh+2\pi r^2=2(\pi rh+\pi r^2)=2(\frac{V}{r}+\frac{V}{h})$ Thanks from greg1313, stgeorge and aurel5
 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: $\displaystyle A=2\sqrt[3]{\frac{V^2\pi}{q}}(1+q)$ Thanks from stgeorge
 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 St-George 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 Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mathsheadache Algebra 5 October 20th, 2014 07:38 PM Thepiman Calculus 2 May 9th, 2014 06:16 AM gdirect Algebra 3 December 11th, 2011 08:59 AM AFireInside Calculus 1 September 10th, 2011 05:30 PM manich44 Algebra 9 October 27th, 2009 02:15 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top