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Volume of Liquid in a Cylindrical Tank

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Date: 05/08/2000 at 23:47:31
From: Mohd Zain Mustapha
Subject: Volume of cylinder

Dear Dr. Math,

I would like to know how to calculate volume of liquid in a cylinder
(not full) lying horizontally.

I appreciate your help very much.

Regards,
Zain
```

```
Date: 05/09/2000 at 08:31:04
From: Doctor Jerry
Subject: Re: Volume of cylinder

Hi Mohd,

Consider a circle of radius a (the end of the tank) and imagine that
the liquid has reached height h, measured from the lowest point on the
circle. Note that  0 <= h <= 2a. The area A of the segment of the
circle covered by the liquid is:

A = pi*a^2/2 - a^2*arcsin(1-h/a) - (a-h)*sqrt(h(2a-h))

The volume of liquid is just A*L, where L is the length of the tank.

- Doctor Jerry, 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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