A sphere is melted and molded into solid cylinder. If radius of both solids are equal, then find the ratio of total surface area of sphere to total surface area of cylinder.

Explanation

Formula used: volume of sphere = (4/3)πr³; total surface area of sphere = 4πr² (r = radius of sphere); volume of cylinder = πR²h; total surface area of cylinder = 2πR(R + h) (R = radius of cylinder, h = height). Given radius of both solids are equal, i.e. R = r. Since the sphere is melted into the cylinder, volume remains same ⇒ (4/3) × (22/7) × r³ = (22/7) × R² × h ⇒ h = 4r/3. Required ratio = 4πr² : 2πR(R + h) = 6 : 7.