If a cylinder has base radius r inches and height h inches then the volume is
V = r2 h cubic inches
When you say you have a cylinder that is 34 " 72" I assume you mean that the diameter of the base is 34" and the height is 72". In this case the radius of the base is 17 " and hence the volume is
V = 172 72 = 65370.3 cubic inches.
There are 231 cubic inches in an american gallon and hence the volume of your cylinder is
65370.3/231 = 283.0 gallons