64 small solid iron spheres of radius 'r' are melted to form a big sphere of radius R. If S and S' are surface areas of the small and the big sphere respectively, then find the ratio S' : S.

16 : 1

64 small solid iron spheres of radius 'r' are melted to form a big sphere of radius R.

Volume of 64 small solid iron spheres of radius 'r' = 4/3 π r^3 * 64

Volume of resultant Large Sphere = 4/3 π R^3 = 4/3 π r^3 * 64

R^3 = 64*r^3

R = 4r

Surface Area of small sphere S = 4πr^2

Surface Area of small sphere S' = 4πR^2 = 4π(4r)^2 = 64πr^2

S':S = 64πr^2 : 4πr^2 = 16:1

The correct answer is Option (3) → 16 : 1