The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Swimming Pool Volume

Date: 02/28/2002 at 11:16:54
From: David Strong
Subject: Cubic feet vs gallons.

What formula would I use to calculate the volume of a swimming pool 
135' x 70' with different depths of 3', 5', 8' and 11'?  


Date: 02/28/2002 at 12:36:27
From: Doctor Peterson
Subject: Re: Cubic feet vs gallons.

Hi, David.

It's not quite clear exactly what shape the pool is; I presume it 
doesn't just drop off suddenly from one depth to another, but slopes 
down from one level to another. Suppose the cross-section looks like 
this, with straight lines within each section:

        a        b          c         d
    |r      |         |           |      |
    |       |s        |           |      |
    +       |         |t          |      |
        \   |         |           |u     |v
            +_____    |           |      |
                  ----+           |      |
                          \       |      |
                              \   |      |

The area of this cross-section will be the sum of four trapezoids, 
each of whose areas is its "height" (width in this case) times the 
average of its two "bases" (depths in this case). The volume of the 
pool is the product of that area and the width perpendicular to this 

So the volume will be

    V = w[a(r+s)/2 + b(s+t)/2 + c(t+u)/2 + d(u+v)/2]

This can be rewritten as

    V = w/2 * [ar + (a+b)s + (b+c)t + (c+d)u + dv]

If the measurements are all in feet, this will give cubic feet. To 
convert to gallons, multiply by 12^3 = 1728 to get cubic inches, and 
divide by 231 cubic inches per gallon.

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

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.