Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

i am so stuck, please help

Answer 6

all right

so a volume of a cylinder is represented by

\[\pi r^2 *h\]

and the surface area is represented by

\[2\pi r^2 +2 \pi r h\]

Answer 7

so we can have the following system of eqn.s

\[\pi r^2h = 192 \pi\]

Answer 8

and

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

Answer 9

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.

\[2\pi r^2 + 2\pi r * {192 \over r^2}= 112\]

Answer 10

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

Answer 11

I can simplify this into\[2\pi r^2 + 384\pi / r = 112\]

so you will get

\[r^3-56r+192 = 0\]

Answer 12

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

Answer 13

what do you mean?

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

Answer 14

i am not sure i am solving for r correctly then, the numbers i am comming up with just don't seem right

Answer 15

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

Answer 16

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

Answer 17

this teacher suks!!

Answer 18

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

Answer 19

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)

Answer 20

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

Answer 21

then the one I just recommended works

Answer 22

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

Answer 23

im still stmuped

Answer 24

what do you mean ?

Answer 25

just use r = 1 and h =192

and r = 1 and h = 55

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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