Area intersection disk and region limit

Let $I$ be the set of points $(x, y)$ in the Cartesian plane such that $$ x > \left( \frac{y^{4}}{9} + 2015 \right)^{1/4} $$ Let $f(r)$ denote the area of the intersection of $I$ and the disk $x^{2} + y^{2} \leq r^{2}$ of radius $r > 0$ centered at the origin $(0,0)$. Determine the minimum possible real number $L$ such that $f(r) < L r^{2}$ for all $r > 0$.