jmc

Let the sphere have radius $r$. A sphere with radius $r$ has surface area $4\pi r^2$, so we have $$324\pi =4\pi r^2.$$ Solving for $r$ and keeping the positive value yields $r^2=81$, so $r=9$. Hence the volume of the sphere is $$\frac{4}{3}\pi (9^3)=81\cdot 3\cdot 4\pi =\boxed{972\pi }.$$