Question : 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.)
Option 1: 6.5 cm
Option 2: 5.5 cm
Option 3: 7.0 cm
Option 4: 6.0 cm
Correct Answer: 5.5 cm
Solution : Given: Radius of sphere $r$ = 8.4 cm The radius of cylinder $R$ = 12 cm Let the height of the cylinder be $h$ cm. According to the question, The volume of the cylinder = volume of the sphere $\pi R^2h = \frac{4}{3}\pi r^3$ ⇒ $12 \times 12 \times h = \frac{4}{3} \times 8.4 \times 8.4 \times 8.4$ ⇒ $h = \frac{4 \times 8.4 \times 8.4 \times 8.4}{3 \times 12 \times 12}$ ⇒ $h = 5.488= 5.5$ (correct to one decimal place) Hence, the correct answer is 5.5 cm.
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