Remember that the surface area of an object is the area of all of its faces added up.
The area of one circle is:
[tex] \pi(4)^2 = 16\pi [/tex]
The area of the rectangle is a little more complex. We are missing the length of one side, which is the circumference of one of the base circles (think about when the diagram above is made into a three-dimensional cylinder). The circumference of the circles is:
[tex] (2 \cdot 4)\pi = 8\pi [/tex]
The area of the rectangle is thus:
[tex] 8\pi \cdot 9 = 72\pi [/tex]
When all of the areas are added together, we find that the total surface area of the shape is:
[tex] 72\pi + 16\pi + 16\pi = \boxed{104\pi} [/tex]
