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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