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Swimming Pool Volume

Date: 07/26/2001 at 03:50:21
From: Jim Majo
Subject: Swimming pool volume

How many gallons will an above-ground 24-foot-diameter pool 48 inches 
tall hold?

Date: 07/26/2001 at 10:52:01
From: Doctor Paul
Subject: Re: Swimming pool volume

The figure you have described is a right circular cylinder. This page 
in our Dr. Math Formulas FAQ


tells you that the formula for the volume is:

   V = Pi * r^2 * h

Here, r = 12 feet (the radius is half the diameter) and h = 4 feet.

So the volume is Pi * 12^2 * 4 = 1809.6 ft^3

Now - how many gallons of water will fit into this pool?

We need to know how many cubic feet of water will fit into one gallon.  
I didn't know this answer off the top of my head, but I found this 
answer in our archives:

   Weight of a Gallon of Water

So it seems that 1 gallon = 3785.4 cm^3

That's almost what we need. We need a conversion between gallons and 
ft^3. So maybe we can convert cm^3 to ft^3.

Since 1 ft = 30.48 cm, we have 1 ft^3 = 30.48^3 cm^3 = 
28316.8 cm^3

So we can write:

1809.6 ft^3   28316.8 cm^3      1 gallon
----------- * ------------ * ----------- =
      1             1 ft^3   3785.4 cm^3

13536.8 gallons of water.

So it looks as if your pool will hold about 13,500  
gallons of water.

I hope this has been clear. Please write back if you have questions 
about how I arrived at any of the above conclusions.

- Doctor Paul, The Math Forum
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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