A solid metallic sphere of radius 8 cm is melted to form 64 equal small solid spheres. The ratio of the surface area of this sphere to that of a small sphere is -

16:1

No. of smaller sphere = \(\frac{volume\;of\;big\;sphere}{volume\;of\;small\;sphere}\)

⇒ 64 = \(\frac{\frac{4}{3} \pi 8^3}{\frac{4}{3} \pi r^3}\)

⇒ r³ = 8

⇒ r = 2 cm

Ratio of surface area ⇒  4 \(\pi \)R² : 4 \(\pi \)r²

                               ⇒  R² : r²

                               ⇒  (8)² : (2)²

                               ⇒  16 : 1