I'm doing a small geometry project with a few different steps. Can somebody please help me? I don't understand this at all and I have to finish by tonight. Thanks!

- anonymous

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- anonymous

what are you having problems with?

- anonymous

I'll post part one

- anonymous

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:
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.

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## More answers

- anonymous

okay

- anonymous

basically you draw a rectangle and you label the shorter side 1400 feet and the longer side 3200 feet

- phi

You should know what "rectangular prism" means
you should know how to find its volume and its surface area
See
http://math.about.com/od/formulas/ss/surfaceareavol_4.htm

- anonymous

why? (I'm trying to understand this at the same time)

- phi

As you see (did you?) you need to find Length L, width W and depth D
they tell you Depth is between 6 and 10 feet
I would pick a number for D as a start

- anonymous

okay does it matter what number? Just any number between 6 and 10?

- phi

It's your design, so you can choose. But I would not pick 6.12378 feet.

- anonymous

Is height the same as depth? Cause you're saying D for depth, but the link you gave me says heigh... Okay, we'll use 10

- phi

Next, what should the shape be? not the actual numbers for length and width, but there ratio. For example, if L=W you would get a square, and (to me) that sounds ugly
*height and depth are the same here. When you talk about a box (rectangular prism) you give it length, width and height. But of course you give a swimming pool depth. But it is the same shape as a box

- phi

or maybe you choose the length to be "olympic size" whatever that is. Google it for numbers

- anonymous

would I write it as something like L=W*3?

- phi

Yes, just write Length will be 3 times the width.
so to summarize you have
D= 10 feet
L= 3W (Length is 3 times the width)
the volume (see link) is V= LWD= 3W*W*10 = 30W^2
we want to do that so we can find W (and then L) after choosing a volume
Volume is between 1400 ft3 and 3200 ft3
we have this equation
V= 30 W^2
or W= \(\sqrt{\frac{V}{30}}\)

- phi

It would be nice to find a "nice" number for W
if we pick a V that is in the middle, and it is divisible by 30, for example 2100 ft3
we find W= sqrt(2100/30)= sqrt(70)
70 does not have a nice square root. But if we use 64, that does.
can you figure out what the volume has to be to get W= sqrt(64)?

- anonymous

1920?

- anonymous

sqrt(1920/30)=sqrt(64)

- anonymous

@phi ?

- phi

so that means 1920 ft3 will give a nice number for W
1920 ft3 meets "spec", so use that.
you get W=8 ft
and L =3W= 24 ft
the volume is LWD= 24*8*10= 1920 ft3 it checks out.

- phi

You have an answer for part I
The dimensions for the Noether pool that fit the above specifications

- phi

Now do part II
The amount of pool liner material that will be needed to completely line the inside of the pool (sides and bottom)
the area of the bottom of the pool (A= L*W)
the area of each side of the pool. Can you figure out the dimensions of each side?
add up the areas of the 4 sides and the bottom to get the grand total.

- anonymous

what do you mean "of each side"?

- phi

they want to know how much liner is used to cover the sides and bottom of the pool.
If you can't visualize this, get a cardboard box and look at it. pretend it is in the ground and is a pool. You should see 4 sides and a bottom

- anonymous

do I just multiply 8*24 twice and add the products, then multiply 10*24 twice and add them all together?

- phi

Did you draw a picture of the pool and label each side?

- anonymous

yes, I got A=864.... Is that correct?

- phi

you are going to make me draw this !?
|dw:1354052145669:dw|

- anonymous

i did that...

- phi

the area of the two ends are each 8*10= 80 or 160 ft2
the area of the long sides 10*24= 240 480 ft2 for both
area of the bottom 8*24= 192 192 ft2 only 1 bottom, no top

- phi

Is that what you got?

- anonymous

so it's 832?

- phi

Did I do it wrong?

- anonymous

(24*8)+(8*10)+(8*10)+(24*10)+(24*10)
192+80+8+240+240
272+320+240
592+240
832
that's how I got 832...

- phi

Yes, I know. It is more mysterious how you got 864

- phi

I guess you were going to put a pool cover on, but leave one of the sides unlined?

- anonymous

I added the wrong numbers, but corrected it after you sent me the right numbers. I mixed up the sides

- anonymous

is 832 right?

- phi

OK, you now have the answer to Part II

- anonymous

how is the 832 written? is it ft? ft^2?

- phi

One reason to learn any of this stuff is not to learn all these details, but to learn how to do a problem and know you are doing it correctly.
area is L*W or W*D etc L is in ft, W is in ft, when you multiply you get ft*ft or ft^2 (square feet)
when you multiply L*W*D you will get ft*ft*ft or ft^3 or cubic ft

- anonymous

so it's ft^2?

- phi

yes it is ft^2

- anonymous

okay next is how much water when the pool is filled .5ft below the top

- phi

now Part III
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
The first thing is figure out the volume (in ft^3) of this. what numbers should we use for L,W and D?

- anonymous

24,8, and 10?

- anonymous

or would it be 9.5?

- phi

if you filled it to a depth of 10 feet that would be too high, don't you think?

- anonymous

so it's 9.5 for W?

- phi

I think of D as the depth

- anonymous

9.5 for D?

- phi

yes Depth is 9.5 ft
|dw:1354053190069:dw|

- anonymous

okay, so I multiply 9.5*8*24 to gget the answer to part 3?

- phi

yes,
and from
http://www.montecitowater.com/how_many_gallons_of_water_in_a_c.htm
you can figure out how many gallons of water that is.
multiply by 7.48 get change ft^3 to gallons. (but I would give both numbers, because some water companies show ft^3 in their bill)

- anonymous

13643.52?

- phi

yes in gallons (you should label your numbers)
1824 cu. ft or 13644 gal.

##### 1 Attachment

- phi

Custom Made by
Sunshine Pools, Inc.

- anonymous

is that it for this step?

- anonymous

@phi ?

- phi

I think you have all the information. Now draw some pictures, and write it up.

- phi

Or was that just Step 1? and there is more to do?

- anonymous

it was just step, but step 2 is to figure out 1/4 those dimmensions (i did that). Now step 3 is (last step, i promise)
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.

- anonymous

I think #1 is a 1:4 ratio....
I don't know #2
#3 is lateral I think because there wasn't a top
#4 I REALLY NEED HELP ON

- phi

What relationship does the volume of the dogs' pool have with the volume of the original family pool?
I would figure out the volume of the smaller pool and then find the ratio of dog vol/pool vol.

- phi

Did you get #1 yet?

- phi

or maybe pool volume / dog volume

- anonymous

yeah, i need help with 2 and 4

- phi

what did you get?

- anonymous

which one?

- phi

pool volume / dog volume

- anonymous

1:4?

- phi

did you calculate the volume of the dog's pool?

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