Answer :

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


Let Ss be the surface area of sphere and Sc be the surface area of cube and Vs be volume of sphere and Vc be volume of cube


Ss = 4πr2 and Sc = 4a2


Given that surface area of sphere and cube are equal


Ss = Sc


4πr2 = 6a2


r2/ a2 = 3/2π



Vs = (4/3) πr3


Vc = a3


Vs/Vc = 4πr3/3a3


Using (i)



Vs/Vc = √21/√11


Therefore ratio of their volumes is Vs:Vc = √21:√11


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