A solid metallic cylinder of base radius 4 cm and height $5\frac{1}{3}$ cm is melted and recast into a sphere. What is the surface area of the sphere, in cm²?

64 π

We know that,

Volume of sphere = \(\frac{4}{3}\)πR³

Surface area of sphere = 4 πR²

Volume of cylinder = πr²h

Radius of cylinder r = 4 cm

We have,

Height of cylinder h = \(\frac{16}{3}\) cm

Now,

\(\frac{4}{3}\) × πR³ = πr²h

R³ = 4 × 4 × \(\frac{16}{3}\) × \(\frac{3}{4}\)

R = 4 cm

Surface area of sphere = 4π × 4² = 64π cm²