A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. Find the dimensi

Question

A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)

 

Radius:

Length:

Answer 1

If the cross section is circular then, the cylinder is cut parallel to the circular base.

22/7* diameter = 132

diameter = 132*7/22 = 42

radius = 21

The rectangular cross section then must obey:

2*(length + diameter) = 132

length + 2*radius = 66

So the constraints are:

radius < 21

length + 2* radius <66

So when the radius varies from 0 < radius < 21,

the length ranges from 24<length<66