The area of a rectangle is width multiplied by length. For the cylinder, the length is the height ( ) and the width is the circumference (because this is the length of the circle) this it is .
Therefore, the surface area considered is .
When , the surface area is at which the price is .
Now consider the surface area when , this would equal .
Now we are able to use general arithmetic (Ratio consideration) to solve for the price. When , therefore the price ( ) is
EDIT: I have attached the cylinder diagram and the net considered.