Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

so whats the answer

Answer 5

what did you get?

Answer 6

idk what you mean really

Answer 7

??????

Answer 8

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

Answer 9

im in grade 9

Answer 10

the answer is supposed to be 5.6cm

Answer 11

what is the height of your cylinder?

Answer 12

No information other than the volume

Answer 13

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

Answer 14

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

Answer 15

algebra grade 9

Answer 16

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

Answer 17

yes,

Answer 18

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

Answer 19

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

Answer 20

oh ok thank you so much i was having trouble.