Volume of Partially Full Cylinder on its Side

Date: 12/31/2001 at 10:03:13
From: Charlie
Subject: Volume of Partially Full Cylinder on its Side 

I am in charge of ordering fuel for our company, and the way the owner 
calculates the volume is via a grossly simplified percent full 
guesstimation. I remember in a college calculus class having to 
calculate the volume of a partially full cylinder (the cylinder being 
on it's side) but I can't remember the equation nor can I find it.
  
Please help.

Date: 12/31/2001 at 11:22:02
From: Doctor Jaffee
Subject: Re: Volume of Partially Full Cylinder on its Side 

Hi Charlie,

Suppose the base of your cylinder is a circle whose radius is r, and 
the height of the fuel in the circle is y.  Let the height of the 
cylinder be h.

Then the volume of fuel can be determined by the formula

                         (r - y)
       V = h[r^2) (arccos -----)( - (r - y)*sqrt(2ry - y^2)]
                            r

This formula is based on the premise that you have your calculator or 
computer software set in the 'radian' mode and not the 'degree' mode.

I hope the formula is helpful to you.

- Doctor Jaffee, The Math Forum
  http://mathforum.org/dr.math/