Our group researched how to make a swimming pool more cost-effective and better for the environment.  We were focused on creating an optimal design that would fit these criteria.  We wanted to reduce the amount of water used, number of tiles used, and amount of money spent.

Step 1: Pyramid Pool: the Pool of the Future (Maybe)

We decided that a pyramid-shaped swimming pool might be better cost-wise and environmentally-wise than a traditional cube or rectangular prism-shaped pool.  The following Steps provide evidence for our reasoning.

Step 2: Calculations for Pool 1

This was the easier pool to find the volume and the surface area,  To find volume, we did length times width times height (12*12*12). To find the surface area, we did found the area of one of the faces (length times width) and multiplied that by the number of faces.  The end surface area equation was 12*12*6.

Step 3: Calculations for Pool 2

Since pool 2 was a pyramid, there were more calculations that needed to be made compared to pool 1.  To find the volume, we did one third base squared times height (1/3*12 squared*12).  As for the surface area, we needed to find additional values in order to find the surface area.  We had to find the height of one of the triangle faces.  To do this, we created a right triangle using the height (12 ft) as one of the legs, and half of the base (6 ft) as the other leg.  From there, we used the Pythagorean Theorem in order to find the length of the hypotenuse (13.42 ft), which was also the height of each triangle face on the pyramid.  With this information, we could find the area of one triangle face and multiply it by 4 to find the surface area of everything but the base.  To find the area of the base, all we had to do was length times width.  By adding the area of the four triangle faces and the area of the square base, we were able to find the surface area of the whole pyramid.  Our final surface area equation looked like this: (12*12)+((1/2*12*13.42)*4).

Step 4: Environmentally Better

A pyramid has 1/3 the volume of a cube, so we can conclude that our proposed pool will use less water.  The average 12' by 12' by 12' cube-shaped swimming pool (Pool 1) has a volume of 12925.44  gallons cubed (1228 feet cubed) and a Surface Area of 864 feet squared.  Our proposed pyramid pool (Pool 2) would have a volume of 4308.48 gallons cubed (576 feet cubed) and a Surface Area of 460.0 feet squared. 

Step 5: Cost Effective

If our pool can save 2/3 the water of a traditional pool, we can probably save a lot of money.  The cost of water for swimming pools is $4.66 per 1,000 gallons ($0.00466 per gallon).  The cost of tile is $21 per square foot.  With this in mind, the water for Pool 1 would cost $60.23 and the tiles would cost $18,144.  With Pool 2, the water would cost $20.08 and the tile would cost $9,786.

Step 6: Head to Head

After comparing the two models, we have determined the following: Pool 2 would save an estimated 8616.96 gallons compared to Pool 1.  Pool 2 would save an estimated 398.0 feet squared in surface area compared to Pool 1.  In terms of cost, Pool 2 would save $40.15 in water, and $8,358.00 in tiles compared to Pool 1.  Considering this information, we have concluded that Pool 2 would be the best choice because of its many benefits such as reduced cost and amount of water saved. 
<p>I didn't read all of the comments to see if anyone pointed this out, so I apologize if it has already been brought up. The volume you calculated on for the &quot;conventional pool&quot; / Pool 1 is 12'x12'x12'. I don't know of any pools that are 12' deep. So your comparison for the volume and cost effectiveness is inaccurate. Good use of math skills to try to solve a problem. Not sure I am ready to buy a deign plan.</p>
-_- Umm... they already do this to an extent, all you had to do to wee it was look at a swimming pool the walls are almost always slanted to conserve water as well as it is very difficult to clean a pool that has a pointed bottom. did I mention the fact that you took something you learned from math class that anyone able to find area could do. Still because its such a simple idea there wont be anyone who could possibly steal it -T3Z
I am spookey bob
I am spookey bob
this is the worst idea I have ever heard of
this is the worst idea I have ever heard of
kids could die in this
i should like to counter these findings with a few questions. first, what is the cost of construction of an angled wall as opposed to a vertical one? there's also the dificulty in digging a pyrimid shaped hole, if it's an in ground pool. <br> <br>aside from construction dificulties, a pool with a pointed bottom and four facets would be very difficult to clean with current cleaning tools. angled walls make it more dificult to stand as well. <br> <br>a final problem with the angled walls is the first thing every child does witha pool. namely jump in. these angled walls make for dangerous edges, and it is almost garenteed that someone willl jump in and hurt htemselves <br> <br>another issue is that a pool is for swimming. and the average adult wont be able to use a two foot ring around the edge of the pool because there isnt enough water. <br> <br>for the purposes of apperant more environmentaly friendly, it has a few perks. however, it's utility makes it less viable.
of appearing more* <br> <br> <br>i really wish i coudl find an edit post button...
Everything looks good if you are constantly swimming in this pool. <br>But if you want to stand and relax for a while.... <br>Maybe you can add a railing around it so you can hang from it. <br>How much would that cost?
judging from the design, i would call this a DIVING pool. <br>as such, it is a most awesome redesign. maximizing depth where it's needed, and eliminating waste. <br> <br>as for hanging or standing, a small lip around the edge would provide plenty of surface for hanging around. <br> <br>The best part, IHMO, is that this design could replace the normal deep end on an olympic style pool. The traditional shallow end where most of the hanging around and such would remain the same. shallow, flat bottom, gentle slope. The new deepend for diving and water polo, etc.as long as the start of the slope were still deep enough. <br> <br>Alternatively, if the design is elongated into a triangular bottomed trough, it would make a pretty decent lap pool, with tons of room for direction changing flips.
As a solution, maybe you can have steps instead of a slope. That would work for standing. <br>

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