Answer
$\dfrac{253 \pi}{20}$
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, $S =\int_{1}^{2} 2 \pi (x) \sqrt {1+\dfrac{(4y^6-1)^2}{16y^6}} dy \\=\int_{1}^{2} 2 \pi \times (y) (\dfrac{4y^6+1}{4y^3} ) dy \\= (\dfrac{\pi}{2}) [\dfrac{4y^3}{3}-y^{-1}]_{1}^{2}\\=\dfrac{253 \pi}{20}$
