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′

(i) Volume of new sphere having radius r’ = πr’3

Volume of 27 spheres having radius r = 27 * πr3


According to the question,


πr’3 = 27 * πr3


= r’3 = 27r3


= r’3 = (3r)3


r’ = 3r


(ii) Ratio =


=


= = 1: 9


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