# Formula for Diameter of Cylinder Using Height/Volume.

1. Mar 22, 2008

### Jordin

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?

Last edited: Mar 22, 2008
2. Mar 22, 2008

### Gib Z

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. Mar 22, 2008

### Gib Z

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

4. Mar 7, 2010

### #38

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. Mar 7, 2010

### #38

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

Last edited: Mar 7, 2010
6. Mar 8, 2010

### HallsofIvy

Staff Emeritus
The volume of a cylinder of height h and radius r is $V= \pi r^2h$.
To solve that for the radius, divide both sides by $\pi h$ 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 $\sqrt{4}= 2$.