Acylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 144 inches. find the dimensions of the package of maximum volume that can be sent. (the cross section is circular.)

The dimensions of the package is .

Step-by-step explanation:

Consider the provided information.

As it is given that, cylindrical package to be sent by a postal service can have a maximum combined length and girth is 144 inches.

Therefore,

144 = 2r + h

144-2r = h

The volume of a cylindrical package can be calculated as:

Substitute the value of h in the above equation.

Differentiate the above equation with respect to r.

Substitute in above equation.

Therefore,

Now, substitute the value of r in 144-2r = h.

Therefore the dimensions of the package should be:

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step-by-step explanation: