A solid metallic sphere of radius 8.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height of the cylinder? (Your answer should be correct to one decimal place.)

5.5 cm

We have,

Radius of sphere = 8.4 cm = r

Radius of cylinder = 12 cm = R

Let the height of the cylinder = h

According to the question,

πR²h = \(\frac{4}{3}\)πr³

12 × 12 × h = \(\frac{4}{3}\) × 8.4 × 8.4 × 8.4

h = \(\frac{4 × 8.4 × 8.4 × 8.4 }{432}\)

h = 5.5