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?
Answer & explanation
Correct answer: option 1
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