Question

A cylindrical can, open at the top, is to hold 500 cm3 of liquid. Find the height and
radius that minimizes the amount of material needed to manufacture the can.

Answer 1

so far I got pi * r^2 * h = 500, h = 500/(pi * r^2).... Don't know the next steps from here.

Answer 2

divide both sides by pi.

Answer 3

leave r and h on one sides. Those are not constant and will vary

Answer 4

And then I think you will need to use a derivative I just don't know eaxctly how

Answer 5

K. So I'm still stuck. I got to thinking that V= pi * r^2 * h = 500 so h = 500/(pi*r^2)
Surface Area = pi*r^2 + 2*pi*r*h.
then yeah I think I do need to take a derivative or something

Answer 6

its optimization. you need to take the volume equation and take the derivative and plug it into your objective equation

Answer 7

@ChukRock Which is the surface area of the object?

Answer 8

surface area = 2(pi)r(h)+2(pi)r

Answer 9

surface area = 2(pi)r(h)+(pi)r^2
I think it's this one.

Answer 10

u sure I need to take the derivative of the volume equation ? with the two variables and h and not the derivative of the surface area with h = 500/(pi*r^2) ?

Answer 11

to be honest i'm not positive cause i dont have my notes with me