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

##### 1 Answer

Feb 27, 2015

First you set up your variables and formulae:

Let

Then girth

Volume

We know that

We will take

We can now express the volume in

To maximise we set the derivative to

Substituting: