Calculus question. A parcel delivery system will deliver a package only if...?

A parcel delivery system will deliver a package only if the length plus girth (distance around) does not exceed 108 inches. What are the radius, length and volume of the largest cylindrical package that may be sent using this service?



I'm having difficulty setting up the equation to solve this since it isn't quite the same as a rectangular box. Any help would be great!Calculus question. A parcel delivery system will deliver a package only if...?
I assume you want to maximize the volume.



Start by defining variables.

Let r denote the radius (in inches) of the cylindrical package

Let h denote the height (in inches) of the cylindrical package



The volume V of a cylinder is given by



V = (蟺/3)r虏h



If r and h are given in inches, then V is in cubic inches.



The length is the height of the cylindrical package; the girth is equal to the circumference of a circle of radius r. We need to have h + 2蟺聽r 鈮?108. Clearly, the volume will be maximized when h + 2蟺聽r is as large as it can be, so we have



h + 2蟺聽r = 108



Solve this for h:



h = 108 - 2蟺聽r



Put this in V:



V = (蟺/3)r虏(108 - 2蟺聽r) = (蟺/3)(108r虏 - 2蟺聽r鲁)



Can you take it from there?