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anonymous

  • 5 years ago

if given just the volume of a cylinder, how do you find the radius and the height so you can build a model???

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  1. Yuki
    • 5 years ago
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    you need more information that just the volume since the volume of a cylinder depends of the radius of the base and the height of the cylinder

  2. Yuki
    • 5 years ago
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    if we know the relationship between the height and the radius, we can figure out what they are

  3. anonymous
    • 5 years ago
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    i have to make either one model that fits both a surface area and volume, or two, one that fits each the only things i have been given to go on a volume wich is 192 times pi(my teacher deoesn't use 3.14) and a total surface area wich is 112 times pi

  4. anonymous
    • 5 years ago
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    i have been working on this for hours and am soooooo frustrated

  5. anonymous
    • 5 years ago
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    i am so stuck, please help

  6. Yuki
    • 5 years ago
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    all right so a volume of a cylinder is represented by \[\pi r^2 *h\] and the surface area is represented by \[2\pi r^2 +2 \pi r h\]

  7. Yuki
    • 5 years ago
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    so we can have the following system of eqn.s \[\pi r^2h = 192 \pi\]

  8. Yuki
    • 5 years ago
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    and \[2\pi r ^2 + 2\pi r h = 112 \pi\]

  9. Yuki
    • 5 years ago
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    all you have to do now is solve the system from the first eqn. \[h = {192 \over r^2}\] if I substitute that in the second eqn. \[2\pi r^2 + 2\pi r * {192 \over r^2}= 112\]

  10. dumbcow
    • 5 years ago
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    V = pi*r^2*h = 192pi SA = 2pi*r^2 +2pi*r*h = 112pi canceling out the pi r^2*h = 192 2(r^2+rh) = 112 from 1st equation h=192/r^2 substitute and solve for r in 2nd equation r^2 +r(192/r^2) = 56 r^2 +192/r = 56 (r^3 +192)/r = 56 r^3-56r +192 = 0 working on seeing if this factors

  11. Yuki
    • 5 years ago
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    I can simplify this into\[2\pi r^2 + 384\pi / r = 112\] so you will get \[r^3-56r+192 = 0\]

  12. anonymous
    • 5 years ago
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    thats pretty much where im at now, but translating that into something i can make a model from i have no idea how to do

  13. Yuki
    • 5 years ago
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    what do you mean? once you solve for r, you just plug that in to the original eqn to find what h is

  14. anonymous
    • 5 years ago
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    i am not sure i am solving for r correctly then, the numbers i am comming up with just don't seem right

  15. dumbcow
    • 5 years ago
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    does not factor using a graph, got approximation r=8.82 so h=2.468

  16. Yuki
    • 5 years ago
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    yea, I tried the rational root theorem but they all failed.

  17. anonymous
    • 5 years ago
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    this teacher suks!!

  18. dumbcow
    • 5 years ago
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    what type of model do you have to do, you could use the relationship between the r and h found to scale any similar cylinder of any size

  19. Yuki
    • 5 years ago
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    if you want to find one that fits only one, then you let r=1 then h =192 if you let h =1 then r = sqrt(192)

  20. anonymous
    • 5 years ago
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    i can make it out of anything, just has to be either one cylinder that has a volume of 192times pi and one that has a surface area of 112 times pi, or one that equals both measurements

  21. Yuki
    • 5 years ago
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    then the one I just recommended works

  22. Yuki
    • 5 years ago
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    one that equals both measures is a tough one because r is not an exact number

  23. anonymous
    • 5 years ago
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    im still stmuped

  24. Yuki
    • 5 years ago
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    what do you mean ?

  25. Yuki
    • 5 years ago
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    just use r = 1 and h =192 and r = 1 and h = 55

  26. dumbcow
    • 5 years ago
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    i made a mistake too the only solution for r is -8.82 not positive so really there is no solution

  27. anonymous
    • 5 years ago
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    thank you yuki and cow, you were both a lot of help

  28. dumbcow
    • 5 years ago
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    go with yuki's idea and pick an h and r to satisfy one of the 2 conditions your welcome

  29. Yuki
    • 5 years ago
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    good luck :) and when you are spending more than 2 hours on your homework, you are pushing yourself too far rest a little, ask your friends, your instructors. and don't forget that we are also here for you

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