Question

You have been hired as contractors for your uncle's company. Your first day on the job you get a call from the Noether family who would like to install a pool in their backyard. Your job is to design the pool and provide some cost estimates.

Answer 1

step 1: 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:

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.

Answer 2

step 2: 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.

Answer 3

step 3: 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.