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

- anonymous

- chestercat

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- 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

if we know the relationship between the height and the radius,
we can figure out what they are

- 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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## More answers

- anonymous

i have been working on this for hours and am soooooo frustrated

- anonymous

i am so stuck, please help

- 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

so we can have the following system of eqn.s
\[\pi r^2h = 192 \pi\]

- yuki

and
\[2\pi r ^2 + 2\pi r h = 112 \pi\]

- 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

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

I can simplify this into\[2\pi r^2 + 384\pi / r = 112\]
so you will get
\[r^3-56r+192 = 0\]

- 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

what do you mean?
once you solve for r, you just plug that in to the original eqn to find what h is

- 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

does not factor
using a graph, got approximation
r=8.82
so
h=2.468

- yuki

yea, I tried the rational root theorem but they all failed.

- anonymous

this teacher suks!!

- 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

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

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

then the one I just recommended works

- yuki

one that equals both measures is a tough one because r is not an exact number

- anonymous

im still stmuped

- yuki

what do you mean ?

- yuki

just use r = 1 and h =192
and r = 1 and h = 55

- dumbcow

i made a mistake too
the only solution for r is -8.82 not positive
so really there is no solution

- anonymous

thank you yuki and cow, you were both a lot of help

- dumbcow

go with yuki's idea and pick an h and r to satisfy one of the 2 conditions
your welcome

- 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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