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

Let radius of sphere = $$r$$ and side of cube = $$a$$ units

According to ques, Surface area of sphere = Surface area of cube

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

=> $$\frac{r^2}{a^2}=\frac{3}{2\pi}$$

=> $$(\frac{r}{a})^3=(\frac{3}{2\pi})^{\frac{3}{2}}$$

$$\therefore$$ Volume of sphere : Volume of cube

= $$\frac{\frac{4}{3}\pi r^3}{a^3}=(\frac{4\pi}{3})(\frac{r}{a})^3$$

= $$\frac{2^2\pi}{3}(\frac{3}{2\pi})^{\frac{3}{2}}$$

= $$\frac{(2)^{2-\frac{3}{2}}(3)^{\frac{3}{2}-1}}{(\pi)^{\frac{3}{2}-1}}$$

= $$\frac{(2)^{\frac{1}{2}}(3)^{\frac{1}{2}}}{(\pi)^{\frac{1}{2}}}$$

= $$\sqrt{6}:\sqrt{\pi}$$

=> Ans - (B)