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### Volume of Partially Full Cylinder on its Side

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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/
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry

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