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) Given that the radius of solid sphere is r and the radius of new sphere is r’.
Volume of solid sphere = 4/3 πr³
Therefore, the volume of 27 solid spheres = 27 × 4/3 πr³
According to question :
Volume of new sphere = volume of 27 solid spheres
⇒ 4/3π (r’)³ = 27 × 4/3πr³
⇒ (r’)³ = 27 × r³
⇒ r’ = 3 × r
Hence, the radius of new sphere is 3r.

(ii) Surface area of new sphere S’ = 4πr²
Surface area of new sphere S’ = 4π(r’)² = 4π(3r)² = 36πr²
Therefore,
s/s’ = 4πr²/36πr² = 1/9
Hence, the ratio of S and S’ is 1:9.