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.
Answer & explanation
Correct answer: option 3
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