Answer
$$\dfrac{28 \sqrt 2 \pi }{3}$$
Work Step by Step
We integrate in order to find the surface area:
$$S= \int_{c}^{d} (2\pi y) \sqrt {1+(y')^2}$$ $$ \\ =2 \pi \times \int_{0}^{3} \sqrt {2x+1} \times \sqrt {\dfrac{2x+2}{2x+1}} dx \\=(2 \sqrt 2) \times (\dfrac{2}{3}) \times (8-1) \pi \\= \dfrac{ \pi (28 \sqrt 2) }{3}$$
