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Sunshine447 Group Title

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!

  • 2 years ago
  • 2 years ago

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  1. momoismyname Group Title
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    what are you having problems with?

    • 2 years ago
  2. Sunshine447 Group Title
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    I'll post part one

    • 2 years ago
  3. Sunshine447 Group Title
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    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.

    • 2 years ago
  4. momoismyname Group Title
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    okay

    • 2 years ago
  5. momoismyname Group Title
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    basically you draw a rectangle and you label the shorter side 1400 feet and the longer side 3200 feet

    • 2 years ago
  6. phi Group Title
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    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

    • 2 years ago
  7. Sunshine447 Group Title
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    why? (I'm trying to understand this at the same time)

    • 2 years ago
  8. phi Group Title
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    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

    • 2 years ago
  9. Sunshine447 Group Title
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    okay does it matter what number? Just any number between 6 and 10?

    • 2 years ago
  10. phi Group Title
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    It's your design, so you can choose. But I would not pick 6.12378 feet.

    • 2 years ago
  11. Sunshine447 Group Title
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    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

    • 2 years ago
  12. phi Group Title
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    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

    • 2 years ago
  13. phi Group Title
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    or maybe you choose the length to be "olympic size" whatever that is. Google it for numbers

    • 2 years ago
  14. Sunshine447 Group Title
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    would I write it as something like L=W*3?

    • 2 years ago
  15. phi Group Title
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    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= \(\sqrt{\frac{V}{30}}\)

    • 2 years ago
  16. phi Group Title
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    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)?

    • 2 years ago
  17. Sunshine447 Group Title
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    1920?

    • 2 years ago
  18. Sunshine447 Group Title
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    sqrt(1920/30)=sqrt(64)

    • 2 years ago
  19. Sunshine447 Group Title
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    @phi ?

    • 2 years ago
  20. phi Group Title
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    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.

    • 2 years ago
  21. phi Group Title
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    You have an answer for part I The dimensions for the Noether pool that fit the above specifications

    • 2 years ago
  22. phi Group Title
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    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.

    • 2 years ago
  23. Sunshine447 Group Title
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    what do you mean "of each side"?

    • 2 years ago
  24. phi Group Title
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    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

    • 2 years ago
  25. Sunshine447 Group Title
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    do I just multiply 8*24 twice and add the products, then multiply 10*24 twice and add them all together?

    • 2 years ago
  26. phi Group Title
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    Did you draw a picture of the pool and label each side?

    • 2 years ago
  27. Sunshine447 Group Title
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    yes, I got A=864.... Is that correct?

    • 2 years ago
  28. phi Group Title
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    you are going to make me draw this !? |dw:1354052145669:dw|

    • 2 years ago
  29. Sunshine447 Group Title
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    i did that...

    • 2 years ago
  30. phi Group Title
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    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

    • 2 years ago
  31. phi Group Title
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    Is that what you got?

    • 2 years ago
  32. Sunshine447 Group Title
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    so it's 832?

    • 2 years ago
  33. phi Group Title
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    Did I do it wrong?

    • 2 years ago
  34. Sunshine447 Group Title
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    (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...

    • 2 years ago
  35. phi Group Title
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    Yes, I know. It is more mysterious how you got 864

    • 2 years ago
  36. phi Group Title
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    I guess you were going to put a pool cover on, but leave one of the sides unlined?

    • 2 years ago
  37. Sunshine447 Group Title
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    I added the wrong numbers, but corrected it after you sent me the right numbers. I mixed up the sides

    • 2 years ago
  38. Sunshine447 Group Title
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    is 832 right?

    • 2 years ago
  39. phi Group Title
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    OK, you now have the answer to Part II

    • 2 years ago
  40. Sunshine447 Group Title
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    how is the 832 written? is it ft? ft^2?

    • 2 years ago
  41. phi Group Title
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    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

    • 2 years ago
  42. Sunshine447 Group Title
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    so it's ft^2?

    • 2 years ago
  43. phi Group Title
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    yes it is ft^2

    • 2 years ago
  44. Sunshine447 Group Title
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    okay next is how much water when the pool is filled .5ft below the top

    • 2 years ago
  45. phi Group Title
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    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?

    • 2 years ago
  46. Sunshine447 Group Title
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    24,8, and 10?

    • 2 years ago
  47. Sunshine447 Group Title
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    or would it be 9.5?

    • 2 years ago
  48. phi Group Title
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    if you filled it to a depth of 10 feet that would be too high, don't you think?

    • 2 years ago
  49. Sunshine447 Group Title
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    so it's 9.5 for W?

    • 2 years ago
  50. phi Group Title
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    I think of D as the depth

    • 2 years ago
  51. Sunshine447 Group Title
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    9.5 for D?

    • 2 years ago
  52. phi Group Title
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    yes Depth is 9.5 ft |dw:1354053190069:dw|

    • 2 years ago
  53. Sunshine447 Group Title
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    okay, so I multiply 9.5*8*24 to gget the answer to part 3?

    • 2 years ago
  54. phi Group Title
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    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)

    • 2 years ago
  55. Sunshine447 Group Title
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    13643.52?

    • 2 years ago
  56. phi Group Title
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    yes in gallons (you should label your numbers) 1824 cu. ft or 13644 gal.

    • 2 years ago
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  57. phi Group Title
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    Custom Made by Sunshine Pools, Inc.

    • 2 years ago
  58. Sunshine447 Group Title
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    is that it for this step?

    • 2 years ago
  59. Sunshine447 Group Title
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    @phi ?

    • 2 years ago
  60. phi Group Title
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    I think you have all the information. Now draw some pictures, and write it up.

    • 2 years ago
  61. phi Group Title
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    Or was that just Step 1? and there is more to do?

    • 2 years ago
  62. Sunshine447 Group Title
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    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.

    • 2 years ago
  63. Sunshine447 Group Title
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    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

    • 2 years ago
  64. phi Group Title
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    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.

    • 2 years ago
  65. phi Group Title
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    Did you get #1 yet?

    • 2 years ago
  66. phi Group Title
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    or maybe pool volume / dog volume

    • 2 years ago
  67. Sunshine447 Group Title
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    yeah, i need help with 2 and 4

    • 2 years ago
  68. phi Group Title
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    what did you get?

    • 2 years ago
  69. Sunshine447 Group Title
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    which one?

    • 2 years ago
  70. phi Group Title
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    pool volume / dog volume

    • 2 years ago
  71. Sunshine447 Group Title
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    1:4?

    • 2 years ago
  72. phi Group Title
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    did you calculate the volume of the dog's pool?

    • 2 years ago
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