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′.
Twenty seven solid iron spheres, each of radius r, are melted to form a bigger sphere of radius r'. It means that combined volume of 27 spheres is equal to volume of new sphere.
Therefore, 27 (volume of 1 sphere of radius r) = Volume of new sphere of radius r'
Surface area of smaller sphere
Surface area of new sphere