Answer
$3 \pi \sqrt 5$
Work Step by Step
The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2}$
Now, $ S=(2 \pi)\int_{1}^{3}(\dfrac{x}{2}+\dfrac{1}{2}) \cdot \sqrt {1+(\dfrac{1}{4})} dy\\= \sqrt 5 \pi \space [\dfrac{x^2}{4}+\dfrac{x^2}{2}] _{1}^{3}\\=3 \pi \sqrt 5$