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The USPS will not mail a package if the sum of its length and its girth (measuring around the package) exceed 108 inches. Determine:
(a) The volume of the package as a function of its radius r.

(b) For which radius r is the volume of the package a maximum?

(c) What is the maximum volume of the package?

  • calculus -

    h = length
    r = radius of cylinder package (I assume)

    girth = 2 pi r

    h + 2pi r = 108 for maximum
    so h = (108-2pir)

    V = pi r^2 h
    V = pi r^2 (108-2 pi r)
    dh/dr = pi r^2 (-2pi) + (108-2 pi r)2pi r
    for max
    2 pi r^2 = 216r - 4 pi r^2
    6 pi r^2 = 216 r
    r = 216/(6 pi)
    r = 11.5
    then h = 108 -2 pi r = 36
    then V = pi r^2 h = 14851 in^3

  • calculus -

    radius? Radius is on spheres. What kind of package are you askig about.

  • calculus -

    The question never specifies the shape of the package so it has really confused me on how to solve it.

  • calculus -

    Well by giving you r, it kind of implies a right circular cylinder.

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