We can calculate the surface area of a cylinder by means of the following cylinder:

Where r is the radius and h the height of the cylinder.
In this case, h equals 6, we are given the diameter of the cylinder instead of its radius, but we can easily find the radius by dividing the diameter by 2:

Now, we just have to replace 6 for h and 4.5 for r into the above equation to get:

Then, the surface area of this cylinder equals 296.73 square inches.