How Many Liters of Water Does a Pool Hold?

Date: 12/4/95 at 2:0:59
From: Anonymous
Subject: Word problem

I have no idea how to even approach this problem:

A swimmer's pool's surface forms a rectangle that measures 25 meters 
long by 15 by 15 meters wide.  The pool is 2 meters deep at the 
shallow end and the depth increases at a constant rate to four 
meters at the other end.  How many liters of water will the pool hold?

Date: 1/18/96 at 11:25:18
From: Doctor Ethan
Subject: Re: Word problem

I will give you an idea how to approach this problem.

A cross section of the pool looks like this.

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~#
#                                 #
#                                 #
#                                 #
 #########                        #
          ########                #
                  ########        #
                          #########

I know the bottom isn't straight, but that is the best that I can do.

So we want to find the area of this shape.  Well, the easiest way to do 
that is to divide it into a rectangle and a triangle.

The upper rectangle has an area of 50 sq. meters and the triangle has an 
area of 25 sq meters.

Do you see how I got that??

Once we have that, then we can multiply it by the width to get the total 
volume.  That should do it.

Hope that this helped.

-Doctor Ethan,  The Geometry Forum