There are many cylinders with a volume of \(144\pi\) cubic inches. The height \(h(r)\), in inches, of one of these cylinders is a function of its radius \(r\), in inches, where \(h(r)=\frac{144}{r^2}\).

1. What is the height of one of these cylinders if its radius is 2 inches?
2. What is the height of one of these cylinders if its radius is 3 inches?
3. What is the height of one of these cylinders if its radius is 6 inches?

The surface area \(S(r)\), in square units, of a cylinder with a volume of 18 cubic units is a function of its radius \(r\), in units, where \(S(r)=2\pi r^2+\frac{36}{r}\). What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units?

Han finds an expression for \(S(r) \) that gives the surface area, in square inches, of any cylindrical can with a specific fixed volume, in terms of its radius \(r\), in inches. This is the graph Han gets if he allows \(r\) to take on any value between -1 and 5.

1. What would be a more appropriate domain for Han to use instead?
2. What is the approximate minimum surface area for the can?