Answer
$4 \pi \sqrt 5$
Work Step by Step
We need to compute the surface area.
$$S= \int_{m}^{n} 2 \pi y \sqrt {1+(y')^2}$$ $$\\=(2 \pi) \times \int_{1}^{4}(\dfrac{x}{2}) \times \sqrt {1+\dfrac{1}{4}} \space dx \\=[\dfrac{\sqrt 5 \pi x^2}{4} ]_1^4\\=4 \pi \sqrt 5$$