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 -
Answer & explanation
Correct answer: option 4
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