Question

Step 1: The Family Pool
The pool should be a rectangular prism. Mrs. Noether wants the pool to hold between 1400 ft3 and 3200 ft3 of water and be from 6-10 feet deep. Other than those specifications, you are free to design the pool how you'd like!

The estimated cost of the pool, besides labor, will come from the pool lining material that coats the inside of the pool and the amount of water needed to fill the pool. Determine the following:

Answer 1

The dimensions for the Noether pool that fit the above specifications
The amount of pool liner material that will be needed to completely line the inside of the pool (sides and bottom)
The amount of water that will be needed to fill the pool if the water needs to be 6 inches below the top of the pool
*Please include the work involved in determining the above measurements or an explanation for how the measurements were determined.

Draft a proposal for the Noethers that includes the above information along with a drawing of their pool. You may need to create more than one drawing to correctly convey your idea.

Step 2: The Dogs' Pool
After you present the plans to the Noethers, Mrs. Noether loves your drawing so much that she wants you to create a similar pool for the family dogs. She wants the dimensions of this pool to be the dimensions of the family pool.

Determine the following:

The dimensions for the dog pool that fit the above specifications
The amount of pool liner material that will be needed to completely line the inside of the pool (sides and bottom)
The amount of water that will be needed to fill the pool if the water needs to be 6 inches below the top of the pool
*Please include the work involved in determining the above measurements or an explanation for how the measurements were determined.

Draft a proposal for the Noethers that includes the above information along with a drawing of their dogs' pool. You may need to create more than one drawing to correctly convey your idea.

Step 3: Questions
Answer the following questions:

What relationship does the volume of the dogs' pool have with the volume of the original family pool? How does this compare to the relationship in the dimensions of the dogs' pool to the dimensions of the family pool?
What is the difference in volume when the pool is filled to the top versus filled to 6 inches below the top?
Was the amount of pool liner material representative of the lateral or surface area of a rectangular prism? Why or why not?
Imagine Mrs. Noether asked you to add steps to the family pool. How would adding steps affect the volume of the water? How would adding steps affect the amount of pool liner material needed? Explain why each change would take place.

Answer 2

Let's make the pool 6 feet deep, 20 feet wide, and 20 feet long.
It will be able to hold 2400f3 of water because the volume of a rectangle =a x b x c

Let's say that the lining, polymer glowing glass, costs 200$ per sq foot. (OUCH!)

Use L x A to find the surface area of each individual side (we can't use the traditional internal surface area formula because we won't need tiling for the top of the pool, if you want to be able to swim, that is)

20x 6 =120
four sides of the pool so
480
Now the bottom of the pool 20x20=400
880 sqf of tiling is needed.
880 x 200(the cost of the polymer glowing glass)
176,000 dollars of tiling (you must be packin the big bucks, huh?)

Okay, so how much water will it take to fill up the pool within 6 inches of the top?
take 6 inches away from 6 ft.
5.5 feet.
5.5x20x20=2200 sq ft (notice for fun that as we took away 1/12 of the height, we lost 1/12 of the total sqr feet)

okay, so you need to fill up 2200 sq ft of pool with water.
After some cunning google use I found out that each sqr foot of pool can hold 7.5 gallons of water.
2200 x 7.481

you're gonna need 16458.2 gallons of water (good luck, ocean)
( you might want to change the numbers a bit)

Answer 3

um do the same for the dogs pool but divide the dimensions by 4