Volume of Liquid in a Cylindrical Tank

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/