Question

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!

Answer 1

what are you having problems with?

Answer 2

I'll post part one

Answer 3

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.

Answer 4

okay

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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= \(\sqrt{\frac{V}{30}}\)

Answer 16

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)?

Answer 17

1920?

Answer 18

sqrt(1920/30)=sqrt(64)

Answer 19

@phi ?

Answer 20

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.

Answer 21

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

Answer 22

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.

Answer 23

what do you mean "of each side"?

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

you are going to make me draw this !?

Answer 29

i did that...

Answer 30

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

Answer 31

Is that what you got?

Answer 32

so it's 832?

Answer 33

Did I do it wrong?

Answer 34

(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...

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

is 832 right?

Answer 39

OK, you now have the answer to Part II

Answer 40

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

Answer 41

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

Answer 42

so it's ft^2?

Answer 43

yes it is ft^2

Answer 44

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

Answer 45

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?

Answer 46

24,8, and 10?

Answer 47

or would it be 9.5?

Answer 48

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

Answer 49

so it's 9.5 for W?

Answer 50

I think of D as the depth

Answer 51

9.5 for D?

Answer 52

yes Depth is 9.5 ft