A piece of paper can be made into a cylinder in two ways: by joining the short sides together, or by joining the long sides together. Which cylinder would hold more? How much more? This is my professors responds when I answered that they were the same just different shapes....
What can we do to show if this is true or not ( figure out how we can show they are the same or not ... what I want is also a mathematical proof - do we have a formula we can use for volume? What information do we need to use it? Do we have that - you may want to make a prototype to test your result). Help Please!

Question

A piece of paper can be made into a cylinder in two ways: by joining the short sides together, or by joining the long sides together. Which cylinder would hold more? How much more?  This is my professors responds when I answered that they were the same just different shapes....
What can we do to show if this is true or not ( figure out how we can show they are the same or not ... what I want is also a mathematical proof - do we have a formula we can use for volume? What information do we need to use it? Do we have that - you may want to make a prototype to test your result). Help Please!