## anonymous 4 years ago a cylinder is being designed to hold rice pudding. it will hold 1078.0 ml of pudding. what radius minimizes the surface area?

1. anonymous

i'm guessing you mean the surface area of the entire cylinder (side and top & bottom) because the rice pudding is only exposed in a disk on top, so a very tall thin cylinder works best to keep your pudding fresh

2. anonymous

$V=\pi r^2 h = 1078$ $SA= 2\pi r^2 + 2\pi r h=2\pi r(r+h)$

3. anonymous

if you have calculus you can use LaGrange Multipliers or take partial derivatives. If you're only working from Algebra 2 then you need to write h in terms of r (or vice versa) using V so that you can minimize a simple graph in one variable.

4. anonymous

5. anonymous

what did you get?

6. anonymous

idk what you mean really

7. anonymous

??????

8. anonymous

are you in calculus? btw my answer was 42*(847pi)^(1/3)

9. anonymous

10. anonymous

the answer is supposed to be 5.6cm

11. anonymous

what is the height of your cylinder?

12. anonymous

No information other than the volume

13. anonymous

yah, i have radius of (539/pi)^(1/3) which is 5.55cm or something

14. anonymous

are you in algebra 2? ie what book is this from , geometry or algebra

15. anonymous

16. anonymous

are you good with Volume = 1078 = (pi) r^2 h ?

17. anonymous

yes,

18. anonymous

because then h = (1078) / (pi r^2) is your value of h which goes into Surface Area = 2*(pi)*r*h + 2*(pi)*r^2

19. anonymous

you're looking for which radius r will minimize surface area, which is 2156/r + 2(pi)r^2

20. anonymous

oh ok thank you so much i was having trouble.