Let r be the radius of sphere and a be the side length of cube.

Let S_s be the surface area of sphere and S_c be the surface area of cube and V_s be volume of sphere and V_c be volume of cube

∴ S_s = 4πr² and S_c = 4a²

Given that surface area of sphere and cube are equal

∴ S_s = S_c

4πr² = 6a²

r²/ a² = 3/2π

V_s = (4/3) πr³

V_c = a³

∴ V_s/V_c = 4πr³/3a³

Using (i)

∴ V_s/V_c = √21/√11

Therefore ratio of their volumes is V_s:V_c = √21:√11