Calculate the volume of the solid $R$ bounded by the two surfaces $z = f(x, y) = 1 - y^2$ and $z = g(x, y) = 3x^2$.
The solid can be described as:
$R = \{(x, y, z) | -\frac{1}{\sqrt{3}} \le x \le \frac{1}{\sqrt{3}}, \underline{\hspace{1cm}} \le y \le \underline{\hspace{1cm}}, \underline{\hspace{1cm}} \le z \le \underline{\hspace{1cm}}\}$,
and its volume is $\underline{\hspace{1cm}}$.