calculus

a. A closed cylindrical can is to hold 1000cm^3 of liquid. How should we choose the height and radius of this can to minimize the amount of material need to manufacture the can?

b.a manufacturer wants to design a open box having a square base and surface of 108cm^2. What dimensions will produce a box with minimum volume?

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asked by dinesh
  1. πr^2 h = 1000, so h = 1000/(πr^2)
    surface area is

    a = 2πr^2 + 2πrh
    = 2πr^2 + 2000/r

    da/dr = 4πr - 2000/r^2
    = 4(πr^3 - 500)/r^2
    da/dr=0 when r = ∛(500/π)
    thus, h = 100/∛(250π)

    Do the other along the same way.

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    posted by Steve
  2. steve bro...
    hw bout the b?
    plz tell me...

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    posted by dinesh
  3. dinesh bro...

    the b is the same as the a

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    posted by Rick
  4. h=234.43

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    posted by dejen
  5. read

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    posted by dejen
  6. answer

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    posted by abebe
  7. -1+x^2

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    posted by abebe

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