Answer
$\dfrac{16\pi }{9} $
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}^{3} 2 \pi (\dfrac{-y^{(3/2)}}{3} +y^{1/2}) [\dfrac{y^{1/2}}{2} +y^{-(1/2)} dy \\=\dfrac{ \pi}{3} [-\dfrac{y^{3}}{3} +y^2+3y]_{1}^{3} \\=\dfrac{16\pi }{9} $
