## 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???

1. anonymous

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. anonymous

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

3. 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

4. anonymous

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

5. anonymous

6. anonymous

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. anonymous

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

8. anonymous

and $2\pi r ^2 + 2\pi r h = 112 \pi$

9. anonymous

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. anonymous

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. anonymous

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

12. 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

13. anonymous

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

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

15. anonymous

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

16. anonymous

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

17. anonymous

this teacher suks!!

18. anonymous

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. anonymous

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

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. anonymous

then the one I just recommended works

22. anonymous

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

23. anonymous

im still stmuped

24. anonymous

what do you mean ?

25. anonymous

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

26. anonymous

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

27. anonymous

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

28. anonymous

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

29. anonymous

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