Three solid metallic sphere whose radii are 3cm, (x) cm and 18cm respectively, are melted and recast into a single solid sphere of diameter 38cm. Then find the total surface area of the sphere with radius (x) cm?

When spheres are melted and recast, total volume remains constant. Volume of sphere = (4/3)πr³. Initial volume = (4/3)π(3³ + x³ + 18³) = (4/3)π(27 + x³ + 5832) = (4/3)π(x³ + 5859). Final sphere has diameter 38 cm, so radius = 19 cm. Its volume = (4/3)π(19)³ = (4/3)π(6859). Equating: x³ + 5859 = 6859, so x³ = 1000, x = 10 cm. Total surface area of sphere with radius x = 4πx² = 4π(100) = 400π, confirming option D.