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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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

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Other answers:

so whats the answer
what did you get?
idk what you mean really
??????
are you in calculus? btw my answer was 42*(847pi)^(1/3)
im in grade 9
the answer is supposed to be 5.6cm
what is the height of your cylinder?
No information other than the volume
yah, i have radius of (539/pi)^(1/3) which is 5.55cm or something
are you in algebra 2? ie what book is this from , geometry or algebra
algebra grade 9
are you good with Volume = 1078 = (pi) r^2 h ?
yes,
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
you're looking for which radius r will minimize surface area, which is 2156/r + 2(pi)r^2
oh ok thank you so much i was having trouble.

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