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math

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the volume of an cylindrical can with a radius r cm and height h cm is 128000 c^3, show that the surface area of the can is A=2(22/7)r^2 + 246000/r. Find the value for r to minimize the surface area.

*i know what the quest. ask but i do not know how to apply it.

  • math -

    It looks like you are being asked to use 22/7 for pi. In that case,
    2(22/7)r^2 is the combined area of the two circular ends.

    If the volume is V = pi*r^2*h, the curved cylindrical area is
    2 pi*r*h = 2V/r.
    That is where your 246000/r term comes from.

    To minimize the surface area, set the derivative of A(r) equal to zero.
    dA/dr = (88/7) r -246,000/r^2 = 0

    r = (246,000*7/88)^1/3 = 26.9 cm

    If you have not yet studied differential calculus, I suggest you graph A vs r and see where it is a mininum.

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