An oil storage tank can be described as the volume generated by revolving the area bounded by $\displaystyle {y}=\frac{{3}}{{\left({4}+{x}^{{2}}\right)}^{{\frac{{1}}{{4}}}}},{x}={0},{y}={0},{x}={4}$ about the x-axis. Find the volume of the tank (in cubic meters).
Round to four decimal places.