anonymous
  • anonymous
if given just the volume of a cylinder, how do you find the radius and the height so you can build a model???
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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yuki
  • yuki
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
yuki
  • yuki
if we know the relationship between the height and the radius, we can figure out what they are
anonymous
  • anonymous
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

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anonymous
  • anonymous
i have been working on this for hours and am soooooo frustrated
anonymous
  • anonymous
i am so stuck, please help
yuki
  • yuki
all right so a volume of a cylinder is represented by \[\pi r^2 *h\] and the surface area is represented by \[2\pi r^2 +2 \pi r h\]
yuki
  • yuki
so we can have the following system of eqn.s \[\pi r^2h = 192 \pi\]
yuki
  • yuki
and \[2\pi r ^2 + 2\pi r h = 112 \pi\]
yuki
  • yuki
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. \[2\pi r^2 + 2\pi r * {192 \over r^2}= 112\]
dumbcow
  • dumbcow
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
yuki
  • yuki
I can simplify this into\[2\pi r^2 + 384\pi / r = 112\] so you will get \[r^3-56r+192 = 0\]
anonymous
  • anonymous
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
yuki
  • yuki
what do you mean? once you solve for r, you just plug that in to the original eqn to find what h is
anonymous
  • anonymous
i am not sure i am solving for r correctly then, the numbers i am comming up with just don't seem right
dumbcow
  • dumbcow
does not factor using a graph, got approximation r=8.82 so h=2.468
yuki
  • yuki
yea, I tried the rational root theorem but they all failed.
anonymous
  • anonymous
this teacher suks!!
dumbcow
  • dumbcow
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
yuki
  • yuki
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)
anonymous
  • anonymous
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
yuki
  • yuki
then the one I just recommended works
yuki
  • yuki
one that equals both measures is a tough one because r is not an exact number
anonymous
  • anonymous
im still stmuped
yuki
  • yuki
what do you mean ?
yuki
  • yuki
just use r = 1 and h =192 and r = 1 and h = 55
dumbcow
  • dumbcow
i made a mistake too the only solution for r is -8.82 not positive so really there is no solution
anonymous
  • anonymous
thank you yuki and cow, you were both a lot of help
dumbcow
  • dumbcow
go with yuki's idea and pick an h and r to satisfy one of the 2 conditions your welcome
yuki
  • yuki
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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