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.)
Answer & explanation
Correct answer: option 3
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