## Introduction: The Swimming Pool Predicament

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.