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May 12th, 2015, 04:20 AM   #1
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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.
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May 12th, 2015, 05:45 AM   #2
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$\displaystyle V=\pi r^2h=r(\pi rh)=>\pi rh=\frac{V}{r}$
$\displaystyle V=\pi r^2h=(\pi r^2)h=>\pi r^2=\frac{V}{h}$
$\displaystyle A=2\pi rh+2\pi r^2=2(\pi rh+\pi r^2)=2(\frac{V}{r}+\frac{V}{h})$
Thanks from greg1313, stgeorge and aurel5
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May 12th, 2015, 09:34 AM   #3
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Wonderful!
Thank you Skaa.
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May 14th, 2015, 05:12 AM   #4
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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.
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May 14th, 2015, 10:37 AM   #5
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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:
$\displaystyle A=2\sqrt[3]{\frac{V^2\pi}{q}}(1+q)$
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May 25th, 2015, 08:39 AM   #6
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Thank you very much once again.
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May 25th, 2015, 09:05 AM   #7
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Do you sell St-George wine?
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May 31st, 2015, 01:03 PM   #8
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Not really Denis
The "St" is part of my Last name, but it's not "Saint". I wish I was one
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June 7th, 2015, 08:42 PM   #9
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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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