Formula for Diameter of Cylinder Using Height/Volume.by Jordin Tags: cylinder, diameter, formula, height or volume 

#1
Mar2208, 01:03 AM

P: 1

I need the formula for finding the Diameter of a Cylinder using it's Volume and Height.
Thanks! Here is the problem. Find Diameter of Cylinder. Volume = 1256.64 Height = 16 Inches Diameter = ? On my own... Knowing Volume = (Pi x Diameter Squared x Height) Divide by 4 I came up with this forumla for D? D = Square Root of (4V/H/Pi) Plugging in the numbers.... D = 10 Inches? Is there an easier forumla? 



#2
Mar2208, 01:12 AM

HW Helper
P: 3,353

Well, what is the Cylinders volume is given by the product of the base circles area and its height. What is the circles area given by, in terms of the radius? How are the radius and diameter related?
PS: Welcome to Physics forums!! =] 



#3
Mar2208, 02:15 AM

HW Helper
P: 3,353

Well you that right, [tex]D= \sqrt{ \frac{4V}{h\pi}}[/tex]. Easiest formula there is lol. Would look nicer in terms of the radius though.




#4
Mar710, 01:57 PM

P: 2

Formula for Diameter of Cylinder Using Height/Volume.
I know this thread is old but it is the only one I could find that is most relevant to my problem.
Can you explain it in terms of the radius? I am trying to figure out the same type of problem and am horrid with roots. I need to find the diameter given H=10m and V=125.6m cubed 



#5
Mar710, 02:29 PM

P: 2

Here is the formula I used to figured it but I think it is wrong.
(I don't know how to do all the fancy stuff so I will just type it out.) v/h over Pi=r squared Edit: I think I got it figured now New formula I am using is v/h*Pi= r squared Find the square root of r squared then multiply * 2 for the diameter 



#6
Mar810, 09:06 AM

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Thanks
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P: 38,879

The volume of a cylinder of height h and radius r is [itex]V= \pi r^2h[/itex].
To solve that for the radius, divide both sides by [itex]\pi h[/itex] and take the square root: [tex]r= \sqrt{\frac{V}{\pi h}[/itex] The diameter is twice the radius, of course, so [tex]d= 2\sqrt{\frac{V}{\pi h}= \sqrt{4V}{\pi h}[/itex] because [itex]\sqrt{4}= 2[/itex]. 


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