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

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:
1.The dimensions for the Noether pool that fit the above specifications
2. The amount of pool liner material that will be needed to completely line the inside of the pool (sides and bottom)
3. 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

@whpalmer4

Answer 3

What do you need help with?

Answer 4

I do not understand how to do this problem. Like how to set it up, what to do

Answer 5

Do you know what a rectangular prism looks like?

Answer 6

yes

Answer 7

Okay. Draw one on a piece of paper and label the length, width, and height with l, w, h. We're going to have to figure out the values. We know that 6 <= h <= 10, and that 1400 <= l*w*h <= 3200 (given in the problem statement).

Answer 8

Now, pick the depth you want the pool to be. It's a rectangular prism, so it will be a uniform depth from end to end.

Answer 9

Ok 8. I basically need you to completely walk me through this question. If u can. I will medal

Answer 10

Oh, boy, I'll do anything for a medal :rolleyes:

Great, so we have a pool that is 8' deep. Now we need to find length and width so that 8*l*w is between 1400 and 3200 cu ft. What would you like the volume to be?

Answer 11

1600 is good

Answer 12

Okay, if the volume = 1600, and the height = 8, what is l*w?

Answer 13

Remember, V = l*w*h

Answer 14

1600/8=200/2

Answer 15

1600/8 = 200, no?

Answer 16

so 100 l and 100 h

Answer 17

Uh, try V = 8*100*100 = ?

Answer 18

that's 80,000

Answer 19

is that between 1400 and 3200? :-)

Answer 20

Ok so those are the dimensions, now about the pool liner

Answer 21

no! answer my question...

Answer 22

and no 80,000 is not in between those two integers

Answer 23

okay, well, that's the volume of the pool you just proposed...

Answer 24

oh so what numbers can we use besides 8. 8x?x?

Answer 25

V = l*w*h
We already chose h = 8, and V = 1600
1600 = l*w*8
Divide both sides by 8
200 = l*w

Pick l and w so that that equation is satisfied...

Answer 26

You did 200 = l + w

Answer 27

8x100x4

Answer 28

200 = 100*4?

Answer 29

no these are new dimensions, could they work

Answer 30

they are 3200

Answer 31

You already chose V = 1600 and h = 8. That means 200 = l*w. If you choose 100 for l and 4 for w, does l*w = 200?

Answer 32

40 and 5

Answer 33

Okay. So we have a pool that is 8 feet deep, 40 feet long, 5 feet wide, and has a volume of 1600 cu ft. Now we need to work out the dimensions of the bottom and 4 sides so we can find their area (the amount of pool liner needed). Put in the dimensions on your diagram. You should have 3 differently sized rectangles — the bottom, the right and left side, and the front and back ends. Can you find the area of each rectangle? You'll add up the area of the bottom, the area of two side rectangles and the area of two end rectangles to get the total area of pool liner required.

Answer 34

so 5 x 8 would be the first one?

Answer 35

What are the dimensions of the bottom?