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Cylinder extreme values

  1. Nov 27, 2006 #1
    I've got kind of stuck with a problem that includes a cylinder.

    First off, we know that the cylinder has a Volume of 100 litre ( V = 100 dm^3 )

    but it get's abit of tricky since you are constructing this cylinder and you are trying to make the cheapest cylinder when the bottom parts of the cylinder costs 10€ / dm^2 and the side parts cost 5€ / dm^2.

    HERE BEGINS MY "WORK"/GUESSING:

    I've come to the conclusion that:

    V = pi*r^2*h

    so: pi*r^2*h = 100
    also this makes: h = 100/ ( pi*r^2 )

    so I figured I'd take:

    10€ * pi*r^2 + 2*pi*r*h*5€

    wich becomes:

    10€ * pi*r^2 + 2*pi*r*100/ (pi*r^2) *5€

    10€ * pi*r^2 + 2*100/r *5€

    then take the derivate of that:

    2*10€ * pi*r - r*1000/r^2

    wich becomes:

    2*10€ * pi*r - 1000/r

    then you make then = 0 or just directly:

    2*10€ * pi*r = 1000/r

    then we try to make out what r is so we mix them around abit:

    20 * pi * r = 1000/r

    r^2 = 1000/(20*pi)

    r = root(1000/(20*pi))

    wich gives:

    r = 3.989422....

    wich it shouldn't, the real answer to r at this point should be something 2.52

    and here is where i'm stuck, any help is appreciated :)
     
    Last edited: Nov 27, 2006
  2. jcsd
  3. Nov 27, 2006 #2
    It should be [tex] \sqrt[3]{\frac{1000}{20\pi}} [/tex]


    The derivative of this is [tex] 20\pi r -\frac{1000}{r^{2}} [/tex] not

    [tex] 20\pi r - \frac{1000r}{r^{2}} [/tex]
     
  4. Nov 28, 2006 #3
    ohh... thanks alot ^.^
     
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