A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)

Length = 47 in

Radius = 47/π in

Step-by-step explanation:

Let 'h' be the length of the package, and 'r' be the radius of the cross section.

The length and girth combined are:

The volume of the cylindrical package is:

Rewriting the volume as a function of 'r':

The value of 'r' for which the derivate of the volume function is zero yields the maximum volume:

The length is:

The dimensions that yield the maximum volume are:

Length = 47 in

Radius = 47/π in

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