Answer
$4 \pi \sqrt 5$
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, $S=\int_{1}^{2} 2 \pi [(2y-1) \sqrt {1+4}] dy = 2\sqrt 5 \pi [y^2-y] _{1}^{2}=4 \pi \sqrt 5$
