A sphere and a cube have equal surface areas. Then the ratio of the volume of the sphere to that of the cube is

Surface area of sphere $=$  Surface area of cube

$4\pi r^2=6a^2$

$a^2=\frac{4\pi r^2}{6}$

$\Rightarrow a=2r\sqrt{\frac{\pi }{6}}$

Volume of sphere :

Volume of cube $=\frac{4}{3}\pi r^3:a^3$

$=\frac{4}{3}\pi r^3:8r^3.\frac{\pi }{6}\frac{\sqrt{\pi }}{\sqrt{6}}$

$=\sqrt{6}:\sqrt{\pi }$