Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S′. Find the
(i) radius r′ of the new sphere, (ii) ratio of S and S′.
Solution:
Here; ratio of volumes = 27 : 1
Radii shall be in sub-triplicate ratio, i.e. 3 : 1
Because 33 : 13 = 27 : 1
Now, surface areas shall be in duplicate ratio of radii
Hence, ratio of surface areas = 32 : 12 = 9 : 1
