Question

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. Determine the following:
The dimensions for the Noether pool that fit the above specifications

Answer 1

Plzz help!

Answer 2

what class is this for?

Answer 3

Geometry

Answer 4

high school?

Answer 5

Yess

Answer 6

you have either not given the correct question or there is no solution to it

Answer 7

is that the exact question on your homework? I can explain why there is no solution if you want

Answer 8

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

Answer 9

Ok nevermind, that is easy. I thought she wanted a pool that could be drained to 6 feet and satisfy the lower volume and filled to 10 feet and satisfy the upper volume. If any pool in that range of depth and volume will work then this is trivial. just give me a second to do it.

Answer 10

ok thanks! :)

Answer 11

I can't seen to upload my pictures right now so i'll just explain it quick

Answer 12

the volume of the pool is given by \[V=lwd\].where l is length w is width and d is depth. You get to choose any volume between 1400 and 3200. Might as well choose V=3200 to make things easy\[3200ft^3=lwd\]ok so now choose a depth. again just choose one that will make things easy. So choose the depth to be 8 feet. Now you have\[3200ft^3=lw(8ft)\]\[3200ft^3/8ft=400ft^2=lw\]Now you can see why I chose those two numbers, you have a nice square there. so just make the length and width the same (l=w) and you can see that \[l^2=400ft^2\]\[l=20ft\]

so the final dimesions of the pool are 8 feet deep by 20 feet long by 20 feet wide.

Answer 13

2) just calculate the surface area of the prism, but remember there is no liner on the top, so subtract that:\[amount=(20ft*20ft)+4(20ft*8ft)=400ft^2+640ft^2=1040ft^2\]
3) If you drain 6" of water you are draining \[v_{drained}=dwl=0.5ft*20ft*20ft=200ft^3\] and then just subtract this from the volume of the full pool\[V_{required}=3200ft^2-200ft^3=3000ft^3\] you could also just do \[7.5ft*20ft*20ft=3000ft^3\]

Answer 14

Just make sure to work through that and check my arithmetic. I have no calculator (not allowed them in my math classes!)