Question 415225
The pool is 3 feet deep at the shallow end and 8 feet deep at the deep end.


If you assume that the pool is all shallow, then the volume would be 20 * 14 * 3 = 840 cubic feet.


That's just for the shallow part.


Take that shallow part away and you are left with a pool that is 5 feet deep.


This part of the pool gradually increases in depth from 0 feet at the shallow to 5 feet at the deep end.


The gradual increase in depth is the diagonal of a rectangle.


This divides the rectangle into 2 triangles that are equal in area to each other.


The area of the pool that is 5 feet deep is 20 * 14 * 5 = 1400 square feet.


half of that is equal to 700 square feet.


The total volume of the water in the pool is 840 + 700 = 1540 cubic feet.


From google, you get 1 cubic foot = 7.48051948 US gallons


Since you have 1540 cubic feet, that equates to 11520 gallons of water.


The average depth of your pool would be 3 feet for the shallow part of the pool plus half of 5 feet for the deeper end of the pool.


That would be equal to 3 + 5/2 = 3 + 2.5 = 5.5 feet.


5.5 * 20 * 14 * 7.48051948 = 11520 gallons of water.


I believe that's how you would do it.


The first 3 feet have to be added to the average of the depth from 3 feet to 8 feet.


The average of the first 3 feet is equal to 3 feet because it does that all the way across.


The depth from 3 feet to 8 is 5 and half of that is 2.5.


the average depth of the pool is therefore 3 + 2.5 = 5.5 feet.


Tricky little problem but I believe that's how you would do it in this case.


Knowing a little geometry helps.


The average depth being half of the low end and the high end applies to only the bottom 5 feet of the pool.