Volume of revolution of an inverse cosine curve

The region bounded by the curve given by $y = 3\cos^{-1}(x)$, for $0 \le y \le a$, where $a > 0$, and the line $x = 0$ is rotated about the $y$-axis to form a solid of revolution. The volume of the solid is $\dfrac{\pi\left(4\pi + 3\sqrt{3}\right)}{8}$.

The value of $a$ is