# Surface Area of a revolution

So I had a question involving Surface Area.

Find the surface area generated by revolving the curve $$x = y^3$$ about the $$y$$-axis for $$0 \leq y \leq \sqrt[4]{11}$$.

(a) $$23\pi\quad$$ (b) $$37\pi\quad$$ (c) $$46\pi\quad$$ (d) $$62\pi\quad$$ (e) $$73\pi\quad$$ (f) None of these

This was my Attempt but I got stuck with trying to integrate the stuff under the radical.

Hint: $$\int y^3(9(y^4+\frac19))^{\frac12}\operatorname dy=\frac32(y^4+\frac19)^{\frac 32}+C$$.