# Hieght of a volume in a cylinder on its side, with known volume.

1. Dec 31, 2007

### GeorgeWBush

This is my first post and is for an applied project (not for a class) but I thought this was the best place to ask for help.

1. The problem statement, all variables and given/known data
Given a cylindar on its side, with volume V, length L, and Radius R, what is height (h) of liquid. I have fomula for volume as a function of radius, length, and height, but when I try to solve for h, things get difficult.

2. Relevant equations

and
http://mathworld.wolfram.com/images/equations/CylindricalSegment/equation2.gif [Broken]

3. The attempt at a solution
1) divide both sides by L
2) square both sides
3) expand polynomials
4) get stuck, post this message

Last edited by a moderator: May 3, 2017
2. Dec 31, 2007

### rocomath

Did you come up with that formula or was it provided and you have to solve for h?

$$\cos^{-1}(\frac{R-h}{R})=\frac{\mbox{adjacent}}{\mbox{hypotenuse}}$$

Last edited: Dec 31, 2007
3. Dec 31, 2007

### GeorgeWBush

It was provided for me and I'm trying to solve for h. It is possible that there is a different approach to the problem that solves for h directly (via caluclus) but I have not found it.